A trader buys a quantity of goods. He sells \frac{1}{4} of the total goods at a profit of … — JAMB UTME

A trader buys a quantity of goods. He sells $\frac{1}{4}$ of the total goods at a profit of $20\%$ , and $\frac{1}{2}$ of the remaining goods at a loss of $10\%$ . If the rest of the goods are sold at cost price, resulting in an overall net profit of $\text{N}1,500$ , what was the total cost price of the goods in Naira?

Cevap: 120000 Naira

Cevap

The total cost price of the goods is 120,000 Naira.

Let

C

be the total cost price of the goods. The first portion sold is

\frac{1}{4}C

at a profit of

20\%

, giving a gain of

0.20 \times \frac{1}{4}C = 0.05C

. The remaining portion is

1 - \frac{1}{4} = \frac{3}{4}C

. Half of this remainder is

\frac{1}{2} \times \frac{3}{4}C = \frac{3}{8}C

, which is sold at a

10\%

loss, causing a loss of

0.10 \times \frac{3}{8}C = 0.0375C

. The final remaining

\frac{3}{8}C

is sold at cost price (0 profit). Thus, the net profit is

0.05C - 0.0375C = 0.0125C

. Setting

0.0125C = 1,500

and solving for

C

gives

C = \frac{1,500}{0.0125} = 120,000

Naira.

Adım Adım Çözüm

Define the unknown total cost price

Let

C

represent the total cost price of the goods in Naira.

Establishing a variable allows for algebraic formulation of profits and losses.

Calculate profit from the first portion

\text{Profit}_1 = 20\% \text{ of } \frac{1}{4}C = 0.20 \times 0.25C = +0.05C

The trader sells a quarter of the total value at a 20% gain.

Determine the remaining quantity and calculate loss from the second portion

\text{Remaining} = C - \frac{1}{4}C = \frac{3}{4}C; \quad \text{Second Portion} = \frac{1}{2} \times \frac{3}{4}C = \frac{3}{8}C = 0.375C; \quad \text{Loss}_2 = 10\% \text{ of } 0.375C = -0.0375C

The second sale applies to half of what was left after the first sale, incurred as a loss.

Equate net profit to given numerical value and solve for total cost price

\text{Net Profit} = 0.05C - 0.0375C = 0.0125C = 1,500 \implies C = \frac{1,500}{0.0125} = 120,000

The rest of the goods were sold at cost price (zero profit/loss), so net profit equals gain from portion 1 minus loss from portion 2.

Anahtar Kavram

Fractions and Percentages of Quantities

Tahmini Süre:1m 30s

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