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Difficulty: MediumCaselets and Paragraph-Based Data

A state public transport corporation operates a total of 500500 buses across three urban divisions: Division X, Division Y, and Division Z. Division X accounts for 40%40\% of the total fleet, Division Y accounts for 30%30\%, and Division Z operates the remaining buses. In Division X, 25%25\% of the buses are electric. In Division Y, the ratio of electric buses to non-electric buses is 2:32 : 3. In Division Z, the number of electric buses is equal to 50%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?

  1. 73 : 27Answer
  2. B
    27 : 73
  3. C
    29 : 21
  4. D
    13 : 7

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%40\% of 500=200500 = 200 buses; Division Y = 30%30\% of 500=150500 = 150 buses; Division Z = 500−(200+150)=150500 - (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%25\% of 200=50200 = 50 buses. Division Y electric = 22+3×150=60\frac{2}{2+3} \times 150 = 60 buses. Division Z electric = 50%50\% of 50=2550 = 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=13550 + 60 + 25 = 135 buses. Total Non-Electric = 500−135=365500 - 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=73:27365 : 135 = 73 : 27.
Simplifying the ratio by dividing both terms by their greatest common divisor, 55.

Key Concept

Caselet Data Extraction and Multi-step Ratio & Percentage Calculations
Estimated Time:1m 30s
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Topics

Caselets and Paragraph-Based Data

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