Data Interpretation Practice Questions — State PSC Exam — Page 3

A vessel contains a mixture of milk and water. What is the initial total volume of the mixture in the vessel?

Statement I: The initial ratio of milk to water in the vessel is $3:2$ . When $10\text{ liters}$ of water is added to the mixture, the ratio of milk to water becomes $1:1$ .
Statement II: If $15\text{ liters}$ of the original mixture is removed and replaced with $15\text{ liters}$ of pure water, the quantity of milk remaining in the vessel is $27\text{ liters}$ .

Which of the following options correctly describes the sufficiency of the statements to answer the question?

Statement I alone is sufficient, but Statement II alone is not sufficient.

Statement II alone is sufficient, but Statement I alone is not sufficient.

Either Statement I alone or Statement II alone is sufficient.

Neither Statement I nor Statement II is sufficient.

Both Statement I and Statement II together are sufficient, but neither statement alone is sufficient.

Show answer & explanation

Answer: Statement I alone is sufficient, but Statement II alone is not sufficient.

Answer

Statement I alone is sufficient to answer the question, but Statement II alone is not sufficient.

Statement I alone gives a complete quantitative relationship: with initial quantities

3x

and

2x

, adding

10\text{ liters}

of water leads to

3x = 2x + 10

, yielding

x = 10

and a unique total initial volume of

50\text{ liters}

. Statement II alone leaves two unknown variables (initial milk fraction and total volume), so it is not sufficient.

Step-by-Step Solution

1

Evaluate Statement I alone.

Initial volume is calculated as

50\text{ liters}

.

Let the initial volume of milk be

3x

liters and water be

2x

liters, making the total initial volume

5x

liters. Adding

10\text{ liters}

of water gives the equation

\frac{3x}{2x + 10} = \frac{1}{1}

, which simplifies to

3x = 2x + 10 \implies x = 10

. Thus, total initial volume

5x = 50\text{ liters}

. Hence, Statement I alone is sufficient.

2

Evaluate Statement II alone.

Insufficient to find total initial volume.

Let the total initial volume be

V

liters and the fraction of milk in the initial mixture be

f

. Removing

15\text{ liters}

of mixture removes

15f

liters of milk. Replacing it with water adds no milk. The remaining milk equation is

f(V - 15) = 27

. Since both

f

and

V

are unknown,

V

cannot be uniquely determined. Hence, Statement II alone is not sufficient.

Key Concept

Data Sufficiency evaluation of mixture ratios and algebraic equations

Estimated Time:1m 30s

Question 42Question →

What is the exact value of the two-digit positive integer $N$ ?

Statement (I): The sum of the tens digit and the units digit of $N$ is equal to $12$ .
Statement (II): Reversing the digits of $N$ yields a new two-digit integer that is $36$ greater than $N$ .

Which of the following statements correctly describes the sufficiency of the given data to answer the question?

Statement (I) alone is sufficient, but Statement (II) alone is not sufficient.

Statement (II) alone is sufficient, but Statement (I) alone is not sufficient.

Either Statement (I) alone or Statement (II) alone is sufficient.

Neither Statement (I) nor Statement (II) is sufficient.

Both Statement (I) and Statement (II) together are sufficient, but neither statement alone is sufficient.

Show answer & explanation

Answer: Both Statement (I) and Statement (II) together are sufficient, but neither statement alone is sufficient.

Answer

Both Statement (I) and Statement (II) together are sufficient to answer the question, but neither statement alone is sufficient.

Evaluating each statement independently reveals that neither statement alone narrows

N

down to a single value. Combining both equations (

x + y = 12

and

y - x = 4

) yields a single unique pair

x = 4

and

y = 8

, giving

N = 48

. Therefore, both statements together are required and sufficient.

Step-by-Step Solution

1

Represent the two-digit integer algebraically.

Let

N = 10x + y

, where

x

is the tens digit (

1 \leq x \leq 9

) and

y

is the units digit (

0 \leq y \leq 9

).

Setting up standard place-value variables allows formal analysis of both statements.

2

Evaluate Statement (I) alone.

From Statement (I),

x + y = 12

. Possible pairs

(x,y)

are

(3,9), (4,8), (5,7), (6,6), (7,5), (8,4), (9,3)

. Thus,

N

could be

39, 48, 57, 66, 75, 84,

or

93

.

Since multiple valid values of

N

exist, Statement (I) alone is NOT sufficient.

3

Evaluate Statement (II) alone.

The reversed number is

10y + x

. Given

(10y + x) - (10x + y) = 36 \implies 9(y - x) = 36 \implies y - x = 4

. Possible pairs

(x,y)

are

(1,5), (2,6), (3,7), (4,8), (5,9)

, giving

N = 15, 26, 37, 48,

or

59

.

Since multiple valid values of

N

exist, Statement (II) alone is NOT sufficient.

4

Evaluate Statement (I) and Statement (II) together.

System of linear equations:

x + y = 12

and

y - x = 4

. Adding the two equations gives

2y = 16 \implies y = 8

. Substituting

y = 8

gives

x = 4

. Thus,

N = 48

uniquely.

Both statements combined provide a unique value for

N

, making them together sufficient.

Key Concept

Data Sufficiency in Digit-Based Integer Problems

Estimated Time:1m 30s

Question 43Question →

In a state sericulture development drive, three agricultural districts—District R, District S, and District T—produced a cumulative total of $3,000\text{ kg}$ of raw silk, consisting exclusively of Mulberry silk and Eri silk. Across all three districts combined, Mulberry silk accounted for $60\%$ of the total raw silk production. In District R, total raw silk production was $1,000\text{ kg}$ , of which $65\%$ was Mulberry silk. District S produced a total of $1,200\text{ kg}$ of raw silk with a Mulberry silk to Eri silk production ratio of $7 : 5$ . The remaining raw silk was produced in District T. What is the absolute difference between the quantity of Mulberry silk and the quantity of Eri silk produced in District T?

100\text{ kg}

150\text{ kg}

200\text{ kg}

50\text{ kg}

Show answer & explanation

Answer: $100\text{ kg}$

Answer

The absolute difference between Mulberry silk and Eri silk produced in District T is

100\text{ kg}

.

Total raw silk produced is

3,000\text{ kg}

, making total Mulberry silk

1,800\text{ kg}

(

60\%

) and total Eri silk

1,200\text{ kg}

. District R produces

650\text{ kg}

Mulberry and

350\text{ kg}

Eri silk. District S produces

700\text{ kg}

Mulberry and

500\text{ kg}

Eri silk. Consequently, District T produces

450\text{ kg}

Mulberry silk (

1,800 - 1,350

) and

350\text{ kg}

Eri silk (

1,200 - 850

). The difference between Mulberry and Eri silk in District T is

450 - 350 = 100\text{ kg}

.

Step-by-Step Solution

1

Calculate overall production totals for Mulberry and Eri silk

Total Mulberry silk =

60\% \text{ of } 3,000\text{ kg} = 1,800\text{ kg}

. Total Eri silk =

3,000\text{ kg} - 1,800\text{ kg} = 1,200\text{ kg}

.

Establishing aggregate category totals provides the basis to determine missing District T values.

2

Determine breakdown for District R and District S

District R: Total =

1,000\text{ kg}

, Mulberry =

65\% \times 1,000 = 650\text{ kg}

, Eri =

350\text{ kg}

. District S: Total =

1,200\text{ kg}

, Mulberry =

\frac{7}{12} \times 1,200 = 700\text{ kg}

, Eri =

\frac{5}{12} \times 1,200 = 500\text{ kg}

.

Extract specific entity values from given percentage and ratio conditions.

3

Derive Mulberry and Eri silk quantities for District T

District T Mulberry =

1,800 - (650 + 700) = 450\text{ kg}

. District T Eri =

1,200 - (350 + 500) = 350\text{ kg}

.

Subtracting known district totals from overall state totals yields District T quantities.

4

Calculate the absolute difference for District T

Difference =

450\text{ kg} - 350\text{ kg} = 100\text{ kg}

.

Directly answers the final prompt query.

Key Concept

Data extraction, multi-entity category balance, and multi-step quantitative calculation from unstructured paragraph data.

Question 44Question →

Under a State Skill Development Mission, a total of $4,500$ candidates were enrolled across three vocational sectors: IT & Electronics, Healthcare & Allied Sciences, and Textile & Apparel. The IT & Electronics sector accounted for $40\%$ of the total enrolled candidates. The ratio of candidates enrolled in Healthcare & Allied Sciences to those in Textile & Apparel was $7 : 8$ . Upon completion of the training, $65\%$ of the enrolled candidates in IT & Electronics successfully obtained certification. The number of certified candidates in Healthcare & Allied Sciences was equal to $80\%$ of the certified candidates in IT & Electronics. If the total number of certified candidates across all three sectors combined was $2,898$ , what percentage of the enrolled candidates in the Textile & Apparel sector successfully obtained certification?

Show answer & explanation

Answer: 55

Answer

The certification percentage of enrolled candidates in the Textile & Apparel sector is

55\%

.

To find the certification percentage for the Textile & Apparel sector, first determine the enrollment figures: IT & Electronics has

1,800

candidates (

40\%

of

4,500

), leaving

2,700

candidates split in a

7 : 8

ratio between Healthcare (

1,260

) and Textile (

1,440

). Next, calculate certified candidates: IT & Electronics has

1,170

certified (

65\%

of

1,800

), and Healthcare has

936

certified (

80\%

of

1,170

). Subtracting these from the total

2,898

certified candidates leaves

792

certified candidates in Textile & Apparel. Finally,

\frac{792}{1,440} \times 100\% = 55\%

.

Step-by-Step Solution

1

Calculate the number of candidates enrolled in IT & Electronics

Enrolled in IT & Electronics =

0.40 \times 4,500 = 1,800

candidates.

IT & Electronics accounts for

40\%

of the overall

4,500

candidates.

2

Determine enrollment in Healthcare & Allied Sciences and Textile & Apparel

Remaining candidates =

4,500 - 1,800 = 2,700

. Enrolled in Healthcare =

\frac{7}{15} \times 2,700 = 1,260

. Enrolled in Textile =

\frac{8}{15} \times 2,700 = 1,440

.

The remaining

2,700

candidates are distributed between Healthcare and Textile in the ratio

7 : 8

(total

15

parts).

3

Calculate certified candidates in IT & Electronics

Certified in IT & Electronics =

0.65 \times 1,800 = 1,170

candidates.

65\%

of the enrolled IT & Electronics candidates achieved certification.

4

Calculate certified candidates in Healthcare & Allied Sciences

Certified in Healthcare =

0.80 \times 1,170 = 936

candidates.

Healthcare certified candidates equal

80\%

of certified candidates in IT & Electronics.

5

Determine certified candidates in Textile & Apparel

Certified in Textile =

2,898 - (1,170 + 936) = 2,898 - 2,106 = 792

candidates.

Total certified across all sectors is

2,898

.

6

Compute the certification rate for Textile & Apparel

Certification percentage =

\left(\frac{792}{1,440}\right) \times 100\% = 55\%

.

Divide certified Textile candidates by total enrolled Textile candidates and convert to percentage.

Key Concept

Data extraction, ratio partitioning, and sequential percentage calculation from unstructured text caselets.

Question 45Question →

Is the integer $x$ odd?

Statement (I): $x^2 + 3x$ is an even integer.
Statement (II): $x + 5$ is an even integer.

Which of the following options is correct?

Statement (I) alone is sufficient, but Statement (II) alone is not sufficient.

Statement (II) alone is sufficient, but Statement (I) alone is not sufficient.

Either Statement (I) alone or Statement (II) alone is sufficient.

Neither Statement (I) nor Statement (II) is sufficient.

Both Statement (I) and Statement (II) together are sufficient, but neither statement alone is sufficient.

Show answer & explanation

Answer: Statement (II) alone is sufficient, but Statement (I) alone is not sufficient.

Answer

Statement (II) alone is sufficient, but Statement (I) alone is not sufficient.

Evaluating Statement (I):

x^2 + 3x = x(x+3)

. The product of any integer

x

and

(x+3)

is always even because one of the two numbers is always even. Thus, Statement (I) provides no specific information about whether

x

is odd or even, making it insufficient. Evaluating Statement (II):

x + 5 = \text{even}

. Subtracting the odd integer

5

from an even integer yields an odd integer, so

x

must be odd. Hence, Statement (II) alone is sufficient to answer the question definitively.

Step-by-Step Solution

1

Evaluate Statement (I) individually.

Rewrite the expression as

x^2 + 3x = x(x + 3)

. If

x

is even, then

x(x + 3) = \text{even} \times \text{odd} = \text{even}

. If

x

is odd, then

x(x + 3) = \text{odd} \times \text{even} = \text{even}

. Thus,

x^2 + 3x

is always even regardless of whether

x

is odd or even.

Since the statement holds true for all integers

x

, it cannot determine whether

x

is odd. Therefore, Statement (I) alone is NOT sufficient.

2

Evaluate Statement (II) individually.

The statement gives that

x + 5

is an even integer. Since

5

is an odd integer,

\text{Odd} + \text{Odd} = \text{Even}

, which implies

x

must be an odd integer.

This yields a definitive 'Yes' answer to the question 'Is

x

odd?'. Therefore, Statement (II) alone IS sufficient.

3

Conclude the data sufficiency evaluation.

Statement (II) alone is sufficient to answer the question, but Statement (I) alone is not sufficient.

Each statement was evaluated independently first, rendering statement combination unnecessary.

Key Concept

Data Sufficiency Parity Analysis

Estimated Time:1m 30s

Question 46Question →

The table below presents the operational performance and energy distribution metrics of four regional power grids during FY 2025–26. Net available energy for distribution is determined by first deducting transmission and storage losses from total generation, and then subtracting auxiliary station consumption.

Regional Grid	Total Energy Generated (GWh)	Transmission & Storage Loss (%)	Auxiliary Station Consumption (GWh)	Commercial Sector Share of Net Available Energy (%)
Northern Grid	12,000	15%	200	40%
Southern Grid	15,000	12%	400	35%
Eastern Grid	10,000	20%	300	50%
Western Grid	18,000	10%	200	25%

Based on the data provided, what is the ratio of the total energy distributed to the commercial sector by the Southern Grid to the combined energy distributed to the commercial sector by the Northern and Western Grids?

14 : 25

97 : 178

154 : 271

21 : 40

Show answer & explanation

Answer: 14 : 25

Answer

The ratio of energy distributed to the commercial sector by the Southern Grid to the combined commercial distribution of the Northern and Western Grids is 14 : 25.

The correct option stating '14 : 25' accurately follows the prescribed two-stage deduction process. For the Southern Grid, subtracting 12% loss (

1,800\text{ GWh}

) from

15,000\text{ GWh}

gives

13,200\text{ GWh}

, and subtracting

400\text{ GWh}

auxiliary consumption leaves

12,800\text{ GWh}

. Applying

35\%

yields

4,480\text{ GWh}

. For the Northern Grid, net energy is

(12,000 - 1,800) - 200 = 10,000\text{ GWh}

, giving

40\% \times 10,000 = 4,000\text{ GWh}

. For the Western Grid, net energy is

(18,000 - 1,800) - 200 = 16,000\text{ GWh}

, giving

25\% \times 16,000 = 4,000\text{ GWh}

. Combining Northern and Western gives

8,000\text{ GWh}

. The ratio

\frac{4,480}{8,000}

simplifies precisely to

14 : 25

.

Step-by-Step Solution

1

Calculate the net available energy and commercial distribution for the Southern Grid.

Net Available =

(15,000 - 0.12 \times 15,000) - 400 = (15,000 - 1,800) - 400 = 12,800\text{ GWh}

. Commercial Distribution =

35\% \text{ of } 12,800 = 4,480\text{ GWh}

.

Transmission loss must be deducted from total generation first, followed by auxiliary consumption.

2

Calculate the net available energy and commercial distribution for the Northern Grid.

Net Available =

(12,000 - 0.15 \times 12,000) - 200 = (12,000 - 1,800) - 200 = 10,000\text{ GWh}

. Commercial Distribution =

40\% \text{ of } 10,000 = 4,000\text{ GWh}

.

Required to compute the combined baseline for Northern and Western grids.

3

Calculate the net available energy and commercial distribution for the Western Grid.

Net Available =

(18,000 - 0.10 \times 18,000) - 200 = (18,000 - 1,800) - 200 = 16,000\text{ GWh}

. Commercial Distribution =

25\% \text{ of } 16,000 = 4,000\text{ GWh}

.

Required to complete the denominator sum of the target ratio.

4

Compute the target ratio of Southern Grid commercial distribution to Northern + Western Grid commercial distribution.

Combined Northern + Western =

4,000 + 4,000 = 8,000\text{ GWh}

. Ratio =

4,480 : 8,000 = 14 : 25

.

Simplifying

\frac{4,480}{8,000}

by dividing both terms by their greatest common divisor

160

yields

14 : 25

.

Key Concept

Multi-step tabular data interpretation involving sequential percentage reduction, absolute deductions, and ratio simplification.

Question 47Question →

A large water reservoir is equipped with two inlet pipes, Pipe $P$ and Pipe $Q$ , each filling the reservoir at its own constant rate. How many hours will it take to fill the empty reservoir if both pipes operate simultaneously from the start?

Statement (I): Pipe $P$ alone can fill the empty reservoir in $15\text{ hours}$ .
Statement (II): Pipe $Q$ fills the reservoir at a rate that is $50\%$ higher than the filling rate of Pipe $P$ .

Which of the following options correctly evaluates the sufficiency of the statements?

Statement (I) alone is sufficient to answer the question, while Statement (II) alone is not sufficient.

Statement (II) alone is sufficient to answer the question, while Statement (I) alone is not sufficient.

Either Statement (I) alone or Statement (II) alone is sufficient to answer the question.

Neither Statement (I) nor Statement (II) is sufficient, and even together they are not sufficient to answer the question.

Both Statement (I) and Statement (II) together are sufficient to answer the question, but neither statement alone is sufficient.

Show answer & explanation

Answer: Both Statement (I) and Statement (II) together are sufficient to answer the question, but neither statement alone is sufficient.

Answer

Both Statement (I) and Statement (II) together are sufficient to answer the question, but neither statement alone is sufficient.

Evaluating Statement (I) alone gives only the individual performance of Pipe P, which is insufficient to determine the combined time. Statement (II) alone provides only a relative ratio between the rates of Pipe P and Pipe Q without any concrete time metric, making it insufficient on its own. When both statements are combined, Statement (I) provides the base rate for Pipe P and Statement (II) allows calculation of Pipe Q's rate, leading to a unique answer of 6 hours for the combined operation.

Step-by-Step Solution

1

Evaluate Statement (I) alone

Pipe

P

's rate is

\frac{1}{15}

of the reservoir per hour. However, no information is given regarding Pipe

Q

's rate.

Statement (I) alone is insufficient to calculate the combined time.

2

Evaluate Statement (II) alone

Pipe

Q

's rate is

1.5

times Pipe

P

's rate, meaning Rate(

Q

)

= 1.5 \times

Rate(

P

).

Statement (II) alone gives only a relative ratio of work rates, with no numerical time value given, so it is insufficient.

3

Evaluate Statements (I) and (II) together

From Statement (I), Rate(

P

)

= \frac{1}{15}

reservoir/hour. From Statement (II), Rate(

Q

)

= 1.5 \times \frac{1}{15} = \frac{1}{10}

reservoir/hour. Combined rate

= \frac{1}{15} + \frac{1}{10} = \frac{1}{6}

reservoir/hour. Thus, total combined time

= 6\text{ hours}

.

Combining both statements yields a unique and definitive answer.

Key Concept

Data Sufficiency in Work and Time / Rate Problems

Question 48Question →

The table below details raw material procurement, fabric output, and sales revenues across four regional textile development clusters for FY 2024–25:

Textile Cluster	Raw Cotton Procured ('000 MT)	Fabric Produced ('000 metres)	Export Value (₹ Crores)	Domestic Sales (₹ Crores)
Cluster A	40	320	160	240
Cluster B	50	500	300	200
Cluster C	60	480	240	360
Cluster D	30	240	180	120

What is the absolute difference (in ₹ Crores) between the average domestic sales across all four clusters and the domestic sales of the cluster that achieved the highest fabric production efficiency per unit of raw cotton procured?

₹30 Crores

₹50 Crores

₹130 Crores

₹30,000

Show answer & explanation

Answer: ₹30 Crores

Answer

The absolute difference is ₹30 Crores.

The correct answer is ₹30 Crores. Fabric production efficiency per unit of raw cotton is calculated as Fabric Produced ('000 metres) divided by Raw Cotton Procured ('000 MT). Cluster B yields 500 / 50 = 10 metres/MT, which is the highest among all clusters (others yield 8 metres/MT). Cluster B's domestic sales are ₹200 Crores. The average domestic sales across all clusters is (240 + 200 + 360 + 120) / 4 = ₹230 Crores. The absolute difference between ₹230 Crores and ₹200 Crores is ₹30 Crores.

Step-by-Step Solution

1

Calculate fabric production efficiency per unit of raw cotton procured for each cluster

Cluster A: 320 / 40 = 8 metres/MT; Cluster B: 500 / 50 = 10 metres/MT; Cluster C: 480 / 60 = 8 metres/MT; Cluster D: 240 / 30 = 8 metres/MT.

To identify which cluster achieved the highest fabric production per unit of raw cotton procured.

2

Identify the domestic sales of the most efficient cluster

Cluster B achieved the highest efficiency (10 metres/MT). Its domestic sales volume is ₹200 Crores.

This provides the targeted cluster's metric for comparison.

3

Calculate the average domestic sales across all four clusters

Total Domestic Sales = 240 + 200 + 360 + 120 = ₹920 Crores. Average Domestic Sales = 920 / 4 = ₹230 Crores.

To determine the benchmark average domestic sales across the dataset.

4

Compute the absolute difference

| ₹230 Crores - ₹200 Crores | = ₹30 Crores.

To answer the final question requirement.

Key Concept

Data grid ratio comparison and benchmark deviation analysis

Question 49Question →

The table below presents the organic horticulture harvest (in metric tonnes) across four agricultural zones in a state for the years 2022 to 2025:

Agricultural Zone	2022	2023	2024	2025
Zone A	320	360	400	480
Zone B	450	500	550	620
Zone C	280	310	350	420
Zone D	550	630	700	780

Based on the table, what is the percentage share of Zone B in the total horticulture harvest across all four agricultural zones combined in the year 2024?

Show answer & explanation

Answer: 27.5

Answer

The percentage share of Zone B in the total horticulture harvest across all four zones combined in 2024 is

27.5\%

.

The total harvest across all four zones in 2024 is

400 + 550 + 350 + 700 = 2000

metric tonnes. Zone B contributed

550

metric tonnes in 2024. Dividing

550

by

2000

and multiplying by

100

yields exactly

27.5\%

.

Step-by-Step Solution

1

Calculate total harvest for all zones in 2024

Total harvest in 2024 =

400 + 550 + 350 + 700 = 2000

metric tonnes

To find the baseline total harvest across all zones for the target year.

2

Locate the specific harvest for Zone B in 2024

Zone B harvest in 2024 =

550

metric tonnes

To isolate the target numerator specified in the question.

3

Compute the percentage share

Percentage share =

\left( \frac{550}{2000} \right) \times 100 = 27.5\%

Dividing the specific zone harvest by the total harvest yields the fractional share, which is converted to percentage by multiplying by 100.

Key Concept

Tabular Percentage Share Calculation

Estimated Time:1m 30s

Question 50Question →

The table below presents the operational metrics for four Inland Freight Terminals in a state for FY 2025–26:

Freight Terminal	Total Cargo Handled (in thousand metric tonnes)	Rail Transshipment Share (%)	Average Dwell Time per Container (days)	Revenue Generated per Tonne (₹)
North	450	40%	4.5	800
South	600	65%	3.0	750
East	350	50%	5.0	900
West	500	30%	6.0	850

What is the total revenue generated from cargo moved specifically via rail transshipment across all four freight terminals combined during FY 2025–26?

₹7.215 crore

₹72.15 crore

₹82.85 crore

₹71.69 crore

Show answer & explanation

Answer: ₹72.15 crore

Answer

₹72.15 crore

To find the total rail transshipment revenue, compute the rail-moved tonnage for each terminal: North (1.80 lakh tonnes), South (3.90 lakh tonnes), East (1.75 lakh tonnes), and West (1.50 lakh tonnes). Multiplying each by its respective revenue per tonne yields ₹14.40 crore, ₹29.25 crore, ₹15.75 crore, and ₹12.75 crore. Summing these four values gives exactly ₹72.15 crore.

Step-by-Step Solution

1

Convert cargo volumes from thousand metric tonnes to tonnes for each terminal

North: 4,50,000 tonnes; South: 6,00,000 tonnes; East: 3,50,000 tonnes; West: 5,00,000 tonnes.

The table header specifies cargo handled in 'thousand metric tonnes'.

2

Calculate the rail transshipment volume for each terminal

North: 4,50,000 × 40% = 1,80,000 tonnes
South: 6,00,000 × 65% = 3,90,000 tonnes
East: 3,50,000 × 50% = 1,75,000 tonnes
West: 5,00,000 × 30% = 1,50,000 tonnes

Rail transshipment share percentage is applied to total cargo volume of each terminal.

3

Compute revenue from rail transshipment for each terminal

North: 1,80,000 × ₹800 = ₹14,40,00,000 (₹14.40 crore)
South: 3,90,000 × ₹750 = ₹29,25,00,000 (₹29.25 crore)
East: 1,75,000 × ₹900 = ₹15,75,00,000 (₹15.75 crore)
West: 1,50,000 × ₹850 = ₹12,75,00,000 (₹12.75 crore)

Multiply rail transshipment tonnes by revenue per tonne.

4

Sum the rail transshipment revenues across all terminals

₹14.40 crore + ₹29.25 crore + ₹15.75 crore + ₹12.75 crore = ₹72.15 crore (₹72,15,00,000).

Total combined rail revenue is the sum of terminal-level rail revenues.

Key Concept

Multi-step weighted calculation from data grids involving unit scale factors and percentages.

Question 51Question →

The table below presents the operational and processing metrics for four municipal water treatment plants in a coastal state for FY 2025–26:

Plant Location	Total Raw Water Processed (Million Liters)	Purified Water Output (%)	Operational Cost per Million Liters (₹ Thousand)
Northern Zone	450	80%	12
Southern Zone	600	85%	10
Eastern Zone	500	78%	15
Western Zone	750	92%	14

Based on the table above, calculate the average volume of purified water output (in Million Liters) produced per plant across the four zones.

Show answer & explanation

Answer: 487.5

Answer

The average volume of purified water output per plant is

487.5

Million Liters.

The purified water volume outputs for Northern, Southern, Eastern, and Western zones are

360

,

510

,

390

, and

690

Million Liters respectively. Summing these values gives a total output of

1950

Million Liters. Dividing this total by the

4

plants gives an average purified water output of

487.5

Million Liters per plant.

Step-by-Step Solution

1

Calculate the purified water volume for each of the four treatment plants

Northern Zone =

360

Million Liters, Southern Zone =

510

Million Liters, Eastern Zone =

390

Million Liters, Western Zone =

690

Million Liters

Purified water output volume is calculated by multiplying Total Raw Water Processed by the Purified Water Output percentage.

2

Sum the purified water volumes across all four zones

Total purified output =

1950

Million Liters

The aggregate sum is required to compute the mean value across all plants.

3

Divide the total purified output by the number of plants (4)

Average purified output =

487.5

Million Liters

Dividing the total sum by the count of entities yields the arithmetic average.

Key Concept

Tabular Data Extraction and Weighted Average Calculation

Question 52Question →

In a municipal solid waste management drive across three processing centers—Plant North, Plant South, and Plant East—a total of $10,000\text{ tonnes}$ of waste was processed in a month.

- Plant North processed $30\%$ of the total waste. Of the waste processed at Plant North, $60\%$ was biodegradable and the rest was non-biodegradable.
- Plant South processed $1.5$ times the amount of non-biodegradable waste processed by Plant North. The ratio of biodegradable to non-biodegradable waste processed at Plant South was $4 : 3$ .
- Plant East processed the remaining waste, with a ratio of biodegradable to non-biodegradable waste of $5 : 2$ .

Based on the information provided above, which of the following statements are correct?

Select all that apply

The total quantity of biodegradable waste processed across all three plants combined is

6,200\text{ tonnes}

.

The ratio of non-biodegradable waste processed by Plant South to that processed by Plant East is

9 : 4

.

Plant East processed

30\%

of the total waste collected across all three plants.

Plant South processed more non-biodegradable waste than the biodegradable waste processed by Plant North.

Show answer & explanation

Answer: The total quantity of biodegradable waste processed across all three plants combined is $6,200\text{ tonnes}$ .; The ratio of non-biodegradable waste processed by Plant South to that processed by Plant East is $9 : 4$ .

Answer

The statements confirming that total biodegradable waste across all plants is 6,200 tonnes and that the ratio of non-biodegradable waste between Plant South and Plant East is 9 : 4 are correct.

The total biodegradable waste is indeed

1,800 + 2,400 + 2,000 = 6,200\text{ tonnes}

, making the first statement correct. Furthermore, comparing non-biodegradable waste of Plant South (

1,800\text{ tonnes}

) and Plant East (

800\text{ tonnes}

) gives the ratio

1,800 : 800 = 9 : 4

, making the second statement correct.

Step-by-Step Solution

1

Calculate waste quantities for Plant North.

Total =

3,000\text{ tonnes}

; Biodegradable =

1,800\text{ tonnes}

; Non-biodegradable =

1,200\text{ tonnes}

.

Plant North processed

30\%

of

10,000\text{ tonnes} = 3,000\text{ tonnes}

. Biodegradable is

60\%

of

3,000 = 1,800\text{ tonnes}

, leaving

1,200\text{ tonnes}

non-biodegradable.

2

Calculate waste quantities for Plant South.

Non-biodegradable =

1,800\text{ tonnes}

; Biodegradable =

2,400\text{ tonnes}

; Total =

4,200\text{ tonnes}

.

Non-biodegradable at South is

1.5 \times 1,200 = 1,800\text{ tonnes}

. Given Bio : Non-bio ratio of

4 : 3

,

3\text{ parts} = 1,800\text{ tonnes} \implies 1\text{ part} = 600\text{ tonnes}

. Thus, Biodegradable =

4 \times 600 = 2,400\text{ tonnes}

.

3

Calculate waste quantities for Plant East.

Total =

2,800\text{ tonnes}

; Biodegradable =

2,000\text{ tonnes}

; Non-biodegradable =

800\text{ tonnes}

.

Remaining total waste =

10,000 - (3,000 + 4,200) = 2,800\text{ tonnes}

. Given Bio : Non-bio ratio of

5 : 2

, total parts =

7

.

1\text{ part} = 400\text{ tonnes}

. Biodegradable =

5 \times 400 = 2,000\text{ tonnes}

and Non-biodegradable =

2 \times 400 = 800\text{ tonnes}

.

4

Verify each statement against calculated values.

Total Biodegradable =

1,800 + 2,400 + 2,000 = 6,200\text{ tonnes}

(True). South Non-bio : East Non-bio =

1,800 : 800 = 9 : 4

(True). Plant East share =

2,800 / 10,000 = 28\%

(False). South Non-bio (

1,800

) vs North Bio (

1,800

) are equal (False).

Comparing calculated numerical values directly evaluates statement validity.

Key Concept

Caselet Data Extraction and Multi-Step Proportionate Allocation

Question 53Question →

A state public transport corporation operates a total of $500$ buses across three urban divisions: Division X, Division Y, and Division Z. Division X accounts for $40\%$ of the total fleet, Division Y accounts for $30\%$ , and Division Z operates the remaining buses. In Division X, $25\%$ of the buses are electric. In Division Y, the ratio of electric buses to non-electric buses is $2 : 3$ . In Division Z, the number of electric buses is equal to $50\%$ of the number of electric buses in Division X. What is the ratio of the total number of non-electric buses to the total number of electric buses across all three divisions combined?

73 : 27

27 : 73

29 : 21

13 : 7

Show answer & explanation

Answer: 73 : 27

Answer

The ratio of the total number of non-electric buses to the total number of electric buses across all three divisions combined is 73 : 27.

Division X has 200 buses with 50 electric buses. Division Y has 150 buses with 60 electric buses (using the 2:3 ratio). Division Z has 150 buses with 25 electric buses (50% of 50). Total electric buses equal 135, leaving 365 non-electric buses. The simplified ratio of non-electric to electric buses is 365 : 135 = 73 : 27.

Step-by-Step Solution

1

Calculate the total fleet size for each division

Division X =

40\%

of

500 = 200

buses; Division Y =

30\%

of

500 = 150

buses; Division Z =

500 - (200 + 150) = 150

buses.

Establishing the total fleet per division is required to extract category values.

2

Calculate electric buses in each division

Division X electric =

25\%

of

200 = 50

buses. Division Y electric =

\frac{2}{2+3} \times 150 = 60

buses. Division Z electric =

50\%

of

50 = 25

buses.

Extracting the electric bus count per division using the specified percentages and ratios.

3

Calculate total electric and non-electric buses combined

Total Electric =

50 + 60 + 25 = 135

buses. Total Non-Electric =

500 - 135 = 365

buses.

Summing values across all divisions to find overall totals.

4

Compute the required ratio of non-electric to electric buses

Ratio =

365 : 135 = 73 : 27

.

Simplifying the ratio by dividing both terms by their greatest common divisor,

5

.

Key Concept

Caselet Data Extraction and Multi-step Ratio & Percentage Calculations

Estimated Time:1m 30s

Question 54Question →

In a state handloom and textile development initiative, data was collected from three handicraft clusters: Cluster A, Cluster B, and Cluster C. A total of $1,200$ weavers are registered across these three clusters. The number of weavers in Cluster C is $300$ , of which $40\%$ are female. The number of weavers in Cluster A is $25\%$ more than the number of weavers in Cluster B. In Cluster B, the ratio of male to female weavers is $3:2$ . If the total number of female weavers across all three clusters is $480$ , what is the total number of male weavers registered in Cluster A?

Show answer & explanation

Answer: 300

Answer

The total number of male weavers registered in Cluster A is 300.

By determining the total weavers in Cluster A (500) and Cluster B (400), and finding the female counts in Cluster C (120) and Cluster B (160), we deduce that Cluster A has 200 female weavers. Subtracting 200 from the 500 total weavers in Cluster A leaves 300 male weavers.

Step-by-Step Solution

1

Determine total weavers in Clusters A and B combined

900 weavers

Subtract Cluster C weavers (300) from the overall total of 1,200 weavers.

2

Calculate weavers in Cluster B and Cluster A

Cluster B = 400 weavers, Cluster A = 500 weavers

Set Cluster A = 1.25 × Cluster B. Then 2.25 × Cluster B = 900, yielding Cluster B = 400 and Cluster A = 500.

3

Determine female weavers in Cluster C and Cluster B

Cluster C females = 120, Cluster B females = 160

40% of 300 is 120 for Cluster C. Based on the 3:2 male to female ratio in Cluster B, females account for 2/5 of 400, which is 160.

4

Calculate female weavers in Cluster A

200 female weavers

Subtract known females in B (160) and C (120) from the total 480 female weavers: 480 - (120 + 160) = 200.

5

Calculate male weavers in Cluster A

300 male weavers

Subtract female weavers in Cluster A from total weavers in Cluster A: 500 - 200 = 300.

Key Concept

Data extraction, multi-step ratio calculation, and percentage breakdown from paragraph caselets.

Question 55Question →

The table below presents the operational and storage metrics for the State Warehousing Corporation across four district hubs for FY 2024–25:

District Hub	Total Storage Capacity ('000 MT)	Actual Grain Stored ('000 MT)	Spoilage Rate (%)	Milling Processing Fee (₹/MT)
Hub Alpha	$250$	$200$	$4\%$	$150$
Hub Beta	$400$	$350$	$2\%$	$120$
Hub Gamma	$300$	$240$	$5\%$	$200$
Hub Delta	$500$	$450$	$3\%$	$100$

Note: $1\text{ MT} = 1\text{ Metric Tonne}$ ; figures in capacity and stored columns are in thousands of MT.

If the government procurement cost of grain is $₹20,000$ per Metric Tonne, what is the total financial loss (in $₹\text{ Lakhs}$ ) incurred due to grain spoilage across Hub Alpha and Hub Gamma combined?

₹4,000\text{ Lakhs}

₹5,000\text{ Lakhs}

₹1,600\text{ Lakhs}

₹4\text{ Lakhs}

Show answer & explanation

Answer: $₹4,000\text{ Lakhs}$

Answer

The total financial loss incurred due to grain spoilage across Hub Alpha and Hub Gamma combined is

₹4,000\text{ Lakhs}

.

To find the total financial loss due to spoilage across Hub Alpha and Hub Gamma, we calculate the spoiled quantity for each hub based on the actual grain stored (in MT):
- Hub Alpha:

200,000\text{ MT} \times 4\% = 8,000\text{ MT}

- Hub Gamma:

240,000\text{ MT} \times 5\% = 12,000\text{ MT}

Total spoiled quantity

= 8,000 + 12,000 = 20,000\text{ MT}

.
At

₹20,000

per MT, total loss

= 20,000 \times 20,000 = ₹400,000,000

. Expressed in Lakhs (

1\text{ Lakh} = 100,000

), this equals

₹4,000\text{ Lakhs}

.

Step-by-Step Solution

1

Calculate the actual quantity of spoiled grain in Hub Alpha

Spoiled grain in Alpha =

4\% \times 200,000\text{ MT} = 8,000\text{ MT}

Actual grain stored in Alpha is

200 \times 1,000 = 200,000\text{ MT}

and spoilage rate is

4\%

.

2

Calculate the actual quantity of spoiled grain in Hub Gamma

Spoiled grain in Gamma =

5\% \times 240,000\text{ MT} = 12,000\text{ MT}

Actual grain stored in Gamma is

240 \times 1,000 = 240,000\text{ MT}

and spoilage rate is

5\%

.

3

Find the combined total quantity of spoiled grain

Total spoiled grain =

8,000\text{ MT} + 12,000\text{ MT} = 20,000\text{ MT}

Combine the spoiled quantities from both hubs.

4

Compute the total financial loss in Rupees and convert to Lakhs

Total Loss =

20,000\text{ MT} \times ₹20,000/\text{MT} = ₹400,000,000 = ₹4,000\text{ Lakhs}

Multiply total spoiled MT by the cost per MT (

₹20,000

) and divide by

100,000

to express in Lakhs.

Key Concept

Data Interpretation from Tables: Multi-step calculation involving unit scale conversion, percentage bases, and aggregation

Question 56Question →

The table below presents the freshwater fish production and pricing metrics across four regional inland lake zones managed by the State Fisheries Development Board for the year 2025:

Lake Zone	Total Catch (in Tonnes)	Export Grade Share (%)	Local Market Price (in ₹ per kg)	Export Market Price (in ₹ per kg)
Lake Alpha	400	30%	150	350
Lake Beta	500	40%	160	400
Lake Gamma	350	20%	140	300
Lake Delta	600	25%	180	420

Note: $1\text{ Tonne} = 1,000\text{ kg}$ and $1\text{ Lakh} = 100,000$ .

Based on the table, calculate the total revenue (in ₹ Lakhs) generated by Lake Beta from both local and export market sales combined.

Show answer & explanation

Answer: 1280

Answer

The total revenue generated by Lake Beta from local and export market sales combined is ₹1,280 Lakhs.

Lake Beta produces

500\text{ tonnes} = 500,000\text{ kg}

of fish.

40\%

of this (

200,000\text{ kg}

) is exported at ₹

400/\text{kg}

, yielding ₹

800\text{ Lakhs}

. The remaining

60\%

(

300,000\text{ kg}

) is sold locally at ₹

160/\text{kg}

, yielding ₹

480\text{ Lakhs}

. Combining both gives ₹

1,280\text{ Lakhs}

.

Step-by-Step Solution

1

Convert the total catch of Lake Beta to kilograms.

500\text{ tonnes} = 500,000\text{ kg}

.

Prices are given per kilogram, so total mass must be in kilograms.

2

Partition the total catch into export grade and local market quantities.

Export quantity =

40\% \times 500,000 = 200,000\text{ kg}

; Local quantity =

60\% \times 500,000 = 300,000\text{ kg}

.

Different market prices apply to export grade vs local grade catch.

3

Calculate monetary revenue for each grade and find their sum in ₹ Lakhs.

Export revenue =

200,000 \times 400 = ₹80,000,000 = ₹800\text{ Lakhs}

; Local revenue =

300,000 \times 160 = ₹48,000,000 = ₹480\text{ Lakhs}

; Total =

800 + 480 = ₹1,280\text{ Lakhs}

.

Summing both revenue streams gives the total earnings for Lake Beta.

Key Concept

Weighted revenue calculation from multi-column tabular data

Estimated Time:1m 30s

Question 57Question →

In a survey of $100$ residents in a locality, $60$ residents read Newspaper X, $50$ read Newspaper Y, and $20$ read both Newspaper X and Newspaper Y. How many residents read neither Newspaper X nor Newspaper Y?

10

20

30

40

Show answer & explanation

Answer: $10$

Answer

The number of residents who read neither Newspaper X nor Newspaper Y is 10.

The total number of residents who read at least one newspaper is given by

N(X \cup Y) = N(X) + N(Y) - N(X \cap Y) = 60 + 50 - 20 = 90

. Thus, the number of residents who read neither newspaper is

100 - 90 = 10

.

Step-by-Step Solution

1

Calculate the number of residents who read at least one newspaper using the Inclusion-Exclusion principle.

|X \cup Y| = 60 + 50 - 20 = 90

Simply adding total readers of X and Y double-counts the residents who read both newspapers.

2

Subtract the number of residents reading at least one newspaper from the total surveyed population.

Neither =

100 - 90 = 10

The universe of residents consists of those reading at least one newspaper and those reading neither.

Key Concept

Principle of Inclusion-Exclusion for two sets

Estimated Time:1m 0s

Question 58Question →

In a survey of $120$ civil service aspirants, $65$ read Newspaper A, $55$ read Newspaper B, and $45$ read Newspaper C. Additionally, $25$ read both A and B, $20$ read both B and C, $15$ read both A and C, and $8$ read all three newspapers. How many aspirants read exactly two of these newspapers?

36

60

52

44

Show answer & explanation

Answer: 36

Answer

36 aspirants read exactly two newspapers.

To find the number of aspirants who read exactly two newspapers, we must subtract the number of aspirants who read all three newspapers (8) from each of the two-newspaper intersection groups. The number of aspirants reading only A and B is

25 - 8 = 17

, only B and C is

20 - 8 = 12

, and only A and C is

15 - 8 = 7

. Summing these exclusive regions gives

17 + 12 + 7 = 36

.

Step-by-Step Solution

1

Identify the given set values and intersections

Total aspirants

N = 120

;

n(A \cap B) = 25

;

n(B \cap C) = 20

;

n(A \cap C) = 15

;

n(A \cap B \cap C) = 8

.

We need to extract overlapping region counts to isolate the 'exactly two' regions.

2

Calculate aspirants reading ONLY two newspapers for each pair

Only A and B =

25 - 8 = 17

; Only B and C =

20 - 8 = 12

; Only A and C =

15 - 8 = 7

.

The given pairwise intersections

n(A \cap B)

include those who read all three newspapers, so

n(A \cap B \cap C)

must be removed from each pair.

3

Sum the exclusive two-set regions

17 + 12 + 7 = 36

.

Adding these three mutually exclusive regions yields the total number of aspirants reading exactly two newspapers.

Key Concept

Venn Diagram set decomposition and region isolation

Question 59Question →

In a survey of $500$ civil service aspirants preparing for State PSC examinations regarding their daily newspaper reading habits:
- $260$ aspirants read Newspaper A
- $220$ aspirants read Newspaper B
- $180$ aspirants read Newspaper C
- $90$ aspirants read both Newspaper A and Newspaper B
- $70$ aspirants read both Newspaper B and Newspaper C
- $80$ aspirants read both Newspaper A and Newspaper C
- $30$ aspirants read all three newspapers

How many aspirants read exactly one of these three newspapers?

180

240

270

420

Show answer & explanation

Answer: $270$

Answer

The number of aspirants who read exactly one newspaper is

270

.

The correct answer is derived by determining the number of readers exclusive to each single newspaper set. Subtracting all overlapping regions (both the exclusive two-paper readers and three-paper readers) from each newspaper's total gives

120

for Newspaper A only,

90

for Newspaper B only, and

60

for Newspaper C only. Adding these exclusive values yields

270

.

Step-by-Step Solution

1

Calculate the number of aspirants who read ONLY Newspaper A, ONLY Newspaper B, and ONLY Newspaper C by isolating two-set and three-set intersections.

Disjoint 2-set intersection counts (excluding all 3 newspapers):
- Reading A and B only:

90 - 30 = 60

- Reading B and C only:

70 - 30 = 40

- Reading A and C only:

80 - 30 = 50

The given two-newspaper intersection counts include the

30

aspirants who read all three newspapers.

2

Subtract the exclusive two-set and three-set intersection counts from each total newspaper count to find single-newspaper readers.

- Only Newspaper A:

260 - (60 + 50 + 30) = 120

- Only Newspaper B:

220 - (60 + 40 + 30) = 90

- Only Newspaper C:

180 - (50 + 40 + 30) = 60

To find readers of 'only' one paper, all overlaps must be subtracted from the total set count.

3

Sum the exclusive counts for Newspaper A, Newspaper B, and Newspaper C.

Total reading exactly one newspaper =

120 + 90 + 60 = 270

These three categories are mutually exclusive, so their sum gives the total count for 'exactly one'.

Key Concept

Principle of Inclusion-Exclusion for Three Sets

Question 60Question →

A survey was conducted among $300$ State PSC aspirants regarding their preparation for three subjects: General Studies ( $GS$ ), General Aptitude Test ( $C$ ), and Optional Subject ( $O$ ). The data collected is as follows:
- $180$ candidates prepare for $GS$
- $140$ candidates prepare for $C$
- $120$ candidates prepare for $O$
- $80$ candidates prepare for both $GS$ and $C$
- $50$ candidates prepare for both $C$ and $O$
- $60$ candidates prepare for both $GS$ and $O$
- $30$ candidates prepare for all three subjects

Which of the following statements are correct? (Select all correct statements)

Select all that apply

The number of candidates preparing for exactly two subjects is

100

.

The number of candidates preparing for at least two subjects is

130

.

The number of candidates preparing for only General Studies (

GS

) is

80

.

The number of candidates who do not prepare for any of the three subjects is

20

.

Show answer & explanation

Answer: The number of candidates preparing for exactly two subjects is $100$ .; The number of candidates preparing for at least two subjects is $130$ .; The number of candidates who do not prepare for any of the three subjects is $20$ .

Answer

The correct statements are those asserting that the number of candidates preparing for exactly two subjects is 100, the number of candidates preparing for at least two subjects is 130, and the number of candidates preparing for none of the three subjects is 20.

The statements asserting that exactly two subjects equal 100, at least two subjects equal 130, and none of the subjects equal 20 are all mathematically accurate based on set region decomposition: exactly two subjects count is

50 + 20 + 30 = 100

; at least two subjects is

100 + 30 = 130

; and outside all sets is

300 - 280 = 20

.

Step-by-Step Solution

1

Identify the central region (all three subjects).

The number of candidates preparing for all three subjects

n(GS \cap C \cap O) = 30

.

This value serves as the base subtraction term for all pairwise intersections.

2

Calculate the counts for candidates preparing for exactly two subjects.

GS and C only =

80 - 30 = 50

; C and O only =

50 - 30 = 20

; GS and O only =

60 - 30 = 30

. Total exactly two subjects =

50 + 20 + 30 = 100

.

Subtracting the triple intersection from each dual intersection isolates regions with exactly two subjects.

3

Calculate candidates preparing for only one subject.

Only GS =

180 - (50 + 30 + 30) = 70

; Only C =

140 - (50 + 30 + 20) = 40

; Only O =

120 - (30 + 30 + 20) = 40

.

Subtracting all overlapping regions from total set cardinalities yields single-subject counts.

4

Calculate the total union and the remainder outside all sets.

Total in at least one subject =

70 + 40 + 40 + 50 + 20 + 30 + 30 = 280

. Neither subject =

300 - 280 = 20

.

Applying inclusion-exclusion principle determines the complete universe coverage.

Key Concept

Three-Set Principle of Inclusion-Exclusion

Estimated Time:2m 0s

Data Interpretation

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