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

$31.25\%$

$26\%$

$52\%$

$35.42\%$

✅ Correct Option: 1

We have three people involved: Minu, Kanu, and Tanu, with the same pair of sunglasses changing hands multiple times.

Minu's initial cost price: Rs. 1000

Minu sells at 20% profit to Kanu.

When we sell at 20% profit, we add 20% of the cost price to the original cost price.

Minu's selling price = 1000 + $\dfrac{20}{100} \times 1000$ = 1000 + 200 = Rs. 1200

Minu's profit from Transaction 1 = Rs. 200

Kanu's cost price: Rs. 1200 (what he paid Minu)

Kanu sells at 20% loss to Minu.

When we sell at 20% loss, we subtract 20% of the cost price from the original cost price.

Kanu's selling price = 1200 - $\dfrac{20}{100} \times 1200$ = 1200 - 240 = Rs. 960

This becomes Minu's new cost price for the sunglasses = Rs. 960

Minu's cost price for second purchase: Rs. 960

Given: Minu's total profit from all transactions = Rs. 500

Minu's profit from Transaction 1: Rs. 200

Therefore, Minu's profit from Transaction 3:

= 500 - 200 = Rs. 300

Minu's selling price to Tanu = 960 + 300 = Rs. 1260

Percentage profit = $\dfrac{\text{Profit}}{\text{Cost price}} \times 100$

Percentage profit when Minu sold to Tanu = $\dfrac{300}{960} \times 100$ = 31.25%

Minu made a 31.25% profit when she sold the sunglasses to Tanu.

In problems involving multiple transactions, we always track each person's cost price and selling price separately. The key is understanding that one person's selling price becomes another person's cost price.

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