CAT 2023 Slot 2 QA Question & Solution
Question
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
Options
Solution
The cost price of the sunglasses for Meenu when he purchased it for the first time was ₹1000.
He sold it to Kanu at a 20% profit, so the selling price becomes:
$$
1000 \times 1.2 = 1200 , \text{rupees}
$$
Hence, the profit made by Meenu in the first transaction is:
$$
1200 - 1000 = 200 , \text{rupees}
$$
Now, the cost price of the same sunglasses for Kanu is ₹1200. He sold it to Meenu at a 20% loss, so the selling price becomes:
$$
1200 \times 0.8 = 960 , \text{rupees}
$$
Thus, the cost price of the sunglasses for Meenu when he purchased it the second time is ₹960.
Meenu then sold it to Tanu at a price such that his total profit becomes ₹500.
The profit made by Meenu in the second transaction is:
$$
500 - 200 = 300 , \text{rupees}
$$
Hence, the percentage profit made by Meenu in the second transaction is:
$$
\frac{300}{960} \times 100 = 31.25%
$$
Therefore, the correct option is C.