CAT 2023

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Profit and Loss — Multi-step transactions, Cost Price & Selling Price relationships
• Formula: $$ \text{Profit %} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100 $$

2. Calculation

Minu's initial cost price (CP₁) for the sunglasses is Rs. 1000.

Transaction 1 — Minu sells to Kanu at 20% profit:

The selling price from Minu to Kanu is: $$ SP_1 = 1000 \times 1.20 = 1200 \text{ rupees} $$

Profit earned by Minu in Transaction 1: $$ \text{Profit}_1 = 1200 - 1000 = \text{Rs. } 200 $$

Transaction 2 — Kanu sells back to Minu at 20% loss:

Kanu's cost price is Rs. 1200. Kanu sells at a 20% loss, so Minu's new buying price (CP₂) is: $$ CP_2 = 1200 \times 0.80 = \text{Rs. } 960 $$

Note that Minu is now the buyer, so this is a cost for her, not a profit.

Transaction 3 — Minu sells to Tanu:

The total profit made by Minu across all transactions is Rs. 500. Since Minu earned Rs. 200 in Transaction 1, the profit she must make in Transaction 3 (selling to Tanu) is: $$ \text{Profit}_3 = 500 - 200 = \text{Rs. } 300 $$

The cost price for this transaction is CP₂ = Rs. 960 (what Minu paid Kanu). So the percentage profit Minu makes when selling to Tanu is: $$ \text{Profit %} = \frac{300}{960} \times 100 = \frac{30000}{960} = 31.25% $$

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3. Solution

Answer = Option C ✅

The percentage profit made by Minu when she sold the sunglasses to Tanu is 31.25%.