CAT 2023 Slot 2 QA Question 9

Multiple choice (+3 / −1) · Arithmetic · Profit & Loss · Try it, then check the answer and solution below.

CAT 2023 Slot 2QAArithmetic • Profit & LossModerate

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

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Official Convenor Answer Key: A

Official Correct Answer: A. First, Minu buys a pair of sunglasses for Rs. 1000. Then she sells it to Kanu at a 20% profit. After that, Kanu sells it back to Minu at a 20% loss. Finally, Minu sells it to Tanu, and the total profit Minu makes from all these transactions is Rs. 500. We find the percentage profit Minu made when she sold to Tanu. Hmm, okay. There are three transactions here: Minu to Kanu, Kanu to Minu, and Minu to Tanu. I need to track the cost price and selling price for each transaction and then figure out the overall profit. Starting with the first transaction: Minu buys the sunglasses for Rs. 1000. So, her cost price (CP1) is Rs. 1000. She sells it to Kanu at a 20% profit. To find the selling price (SP1), I can calculate 20% of 1000 and add it to the CP. So, 20% of 1000 is (20/100)*1000 = 200. Therefore, SP1 = 1000 + 200 = Rs. 1200. So, Minu sells it to Kanu for Rs. 1200, making a profit of Rs. 200. Now, Kanu buys it for Rs. 1200 and then sells it back to Minu at a 20% loss. Wait, 20% loss on what? Is it on Kanu's cost price or on Minu's original price? I think it's on Kanu's cost price because when you sell something at a loss, it's usually based on your own cost. So, Kanu's cost price is Rs. 1200, and he sells it at a 20% loss. Calculating 20% of 1200: (20/100)*1200 = 240. So, the selling price (SP2) from Kanu to Minu is 1200 - 240 = Rs. 960. So, Minu buys it back from Kanu for Rs. 960. Let me summarize the transactions so far: 1. Minu buys at 1000, sells at 1200 (Profit: 200) 2. Kanu buys at 1200, sells at 960 (Loss: 240) 3. Minu buys at 960, sells at ? (Profit: ?) Now, Minu sells it to Tanu. Let's denote the selling price as SP3. The total profit Minu makes from all transactions is Rs. 500. So, We calculate Minu's total profit from all three transactions and set it equal to 500. Calculating Minu's profit step by step. First transaction: Minu sold at 1200, bought at 1000. Profit: 200. Second transaction: Minu bought at 960, sold at 1200? Wait, no. Wait, in the second transaction, Minu bought back from Kanu at 960. So, Minu's cost price for the third transaction is 960. She then sells it to Tanu at SP3. So, Minu's profit from the third transaction is SP3 - 960. Now, total profit is the sum of profits from all transactions. But wait, Minu only made two transactions where she was selling: the first and the third. The second transaction was buying, so it's a cost, not a profit. Wait, let me clarify. Minu's total profit is the sum of profits from selling minus the costs from buying. So, she sold twice: first at 1200, then at SP3. She bought twice: first at 1000, then at 960. So, her total profit would be (1200 - 1000) + (SP3 - 960) - (960 - 1200). Wait, no, that's not right. Wait, no, she bought at 1000, sold at 1200: profit 200. Then she bought at 960, sold at SP3: profit (SP3 - 960). So, total profit is 200 + (SP3 - 960). But she also had a cost when she bought back from Kanu, which was 960, but that's already included in the second term. Wait, maybe I should think of it as overall. Minu started with 1000, sold for 1200, then bought back for 960, then sold for SP3. So, her total cost is 1000 + 960, and her total revenue is 1200 + SP3. So, total profit is (1200 + SP3) - (1000 + 960) = 1200 + SP3 - 1960 = SP3 - 760. But the total profit is given as 500, so SP3 - 760 = 500. Therefore, SP3 = 500 + 760 = 1260. Wait, that seems straightforward. So, SP3 is 1260. Then, Minu sold to Tanu at 1260. Her cost price for that transaction was 960, so the profit amount is 1260 - 960 = 300. To find the percentage profit, it's (Profit / Cost Price) * 100. So, (300 / 960) * 100. Calculating that: 300 divided by 960. Let's simplify. Both numerator and denominator can be divided by 60: 300/60=5, 960/60=16. So, 5/16. 5 divided by 16 is 0.3125. Multiply by 100: 31.25%. So, the percentage profit is 31.25%, which is option A. 1. Minu buys at 1000, sells at 1

Answer and solution

Answer: A) $31.25\%$

First, Minu buys a pair of sunglasses for Rs.

1000

Then she sells it to Kanu at a 20% profit. After that, Kanu sells it back to Minu at a 20% loss. Finally, Minu sells it to Tanu, and the total profit Minu makes from all these transactions is Rs.

500

We find the percentage profit Minu made when she sold to Tanu.

Hmm, okay. There are three transactions here: Minu to Kanu, Kanu to Minu, and Minu to Tanu. I need to track the cost price and selling price for each transaction and then figure out the overall profit.

Starting with the first transaction: Minu buys the sunglasses for Rs.

1000

So, her cost price (CP1) is Rs.

1000

She sells it to Kanu at a 20% profit. To find the selling price (SP1), I can calculate 20% of 1000 and add it to the CP.

So, 20% of 1000 is (20/100)*1000 = 200. Therefore, SP1 = 1000 + 200 = Rs.

1200

So, Minu sells it to Kanu for Rs. 1200, making a profit of Rs.

200

Now, Kanu buys it for Rs. 1200 and then sells it back to Minu at a 20% loss. Wait, 20% loss on what? Is it on Kanu's cost price or on Minu's original price? I think it's on Kanu's cost price because when you sell something at a loss, it's usually based on your own cost. So, Kanu's cost price is Rs. 1200, and he sells it at a 20% loss.

Calculating 20% of 1200: (20/100)*1200 = 240. So, the selling price (SP2) from Kanu to Minu is 1200 - 240 = Rs.

960

So, Minu buys it back from Kanu for Rs.

960

Let me summarize the transactions so far:

Minu buys at 1000, sells at 1200 (Profit: 200)

Kanu buys at 1200, sells at 960 (Loss: 240)

Minu buys at 960, sells at ? (Profit: ?)

Now, Minu sells it to Tanu. Let's denote the selling price as SP3. The total profit Minu makes from all transactions is Rs.

500

So, We calculate Minu's total profit from all three transactions and set it equal to 500.

Calculating Minu's profit step by step.

First transaction: Minu sold at 1200, bought at 1000. Profit:

200

Second transaction: Minu bought at 960, sold at 1200? Wait, no. Wait, in the second transaction, Minu bought back from Kanu at 960. So, Minu's cost price for the third transaction is 960. She then sells it to Tanu at SP3.

So, Minu's profit from the third transaction is SP3 - 960.

Now, total profit is the sum of profits from all transactions. But wait, Minu only made two transactions where she was selling: the first and the third. The second transaction was buying, so it's a cost, not a profit.

Wait, let me clarify. Minu's total profit is the sum of profits from selling minus the costs from buying. So, she sold twice: first at 1200, then at SP3. She bought twice: first at 1000, then at 960.

So, her total profit would be (1200 - 1000) + (SP3 - 960) - (960 - 1200). Wait, no, that's not right. Wait, no, she bought at 1000, sold at 1200: profit 200. Then she bought at 960, sold at SP3: profit (SP3 - 960). So, total profit is 200 + (SP3 - 960). But she also had a cost when she bought back from Kanu, which was 960, but that's already included in the second term.

Wait, maybe I should think of it as overall. Minu started with 1000, sold for 1200, then bought back for 960, then sold for SP3. So, her total cost is 1000 + 960, and her total revenue is 1200 + SP3. So, total profit is (1200 + SP3) - (1000 + 960) = 1200 + SP3 - 1960 = SP3 - 760.

But the total profit is given as 500, so SP3 - 760 = 500. Therefore, SP3 = 500 + 760 = 1260.

Wait, that seems straightforward. So, SP3 is 1260. Then, Minu sold to Tanu at 1260. Her cost price for that transaction was 960, so the profit amount is 1260 - 960 = 300.

To find the percentage profit, it's (Profit / Cost Price) 100. So, (300 / 960) 100.

Calculating that: 300 divided by 960. Let's simplify. Both numerator and denominator can be divided by 60: 300/60=5, 960/60=16. So, 5/16. 5 divided by 16 is 0.3125. Multiply by 100: 31.25%.

So, the percentage profit is 31.25%, which is option A.

Minu buys at 1000, sells at 1

CAT 2023 Slot 2 QA Question 9

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