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CAT 2023 Slot 2 — QA Question 11

Profit & LossEasy

Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

Answer & solution

  • A

    26%

  • 31.25%

  • C

    52%

  • D

    35.42%

Solution

Easy

Track Minu's money through three deals. Her profit on the Kanu sale is locked in; the buy-back gives her a new cost price; the final sale to Tanu must top up her total profit to 500500. The profit %\% is always measured on the cost price for that sale.

1

Minu sells to Kanu at 20%20\% profit on 10001000:

Sale=1000×1.2=1200Profit so far=1200−1000=200\begin{aligned} &\text{Sale}=1000\times1.2=1200\\ &\text{Profit so far}=1200-1000=200 \end{aligned}
2

Kanu sells back to Minu at 20%20\% loss on 12001200. This becomes Minu's new cost:

Buy-back=1200×0.8=960\begin{aligned} &\text{Buy-back}=1200\times0.8=960 \end{aligned}
3

Find the profit needed on the Tanu sale. Total profit must reach 500500:

200+(Tanu profit)=500⇒ Tanu profit=300\begin{aligned} &200+(\text{Tanu profit})=500\\ &\Rightarrow\ \text{Tanu profit}=300 \end{aligned}
4

Profit %\% on the Tanu sale uses Minu's cost of 960960:

300960×100%=31.25%\begin{aligned} &\frac{300}{960}\times100\%=31.25\% \end{aligned}

Minu's profit on the sale to Tanu is 31.25%\mathbf{31.25\%}.

The trap is dividing 300300 by 10001000 (the original cost) instead of 960960 (her cost just before selling to Tanu). Each sale's profit %\% is reckoned on that sale's own cost price.

CAT 2023 Slot 2 QA Q11: Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Mi — Solution | TheCATExam