A sold two items, X and Y, at 25% and 35% profit, respectively. If the difference between their profit is Rs 750 and the cost price of both items is the same, find the cost price of item X.

The correct answer is Rs 7500.

We are told that A sold two items, X and Y, at 25% profit and 35% profit respectively, the difference in their profits is Rs 750, and both items have the same cost price. We need to find the cost price of item X.

Step 1: Set up a variable.

Let the cost price of both items X and Y be Rs C (since both have the same cost price).

Step 2: Express the profit earned on each item.

Profit on item X (sold at 25% profit):

P_X=\frac{25}{100}\times C=0.25C

Profit on item Y (sold at 35% profit):

P_Y=\frac{35}{100}\times C=0.35C

Step 3: Use the condition that the difference in their profits is Rs 750.

Since Y is sold at a higher profit percentage, Y's profit exceeds X's profit:

P_Y-P_X=750

0.35C-0.25C=750

0.10C=750

Step 4: Solve for C.

C=\frac{750}{0.10}=7500

Step 5: Verify the answer.

With cost price = Rs 7500:
- Profit on X at 25% = 0.25 × 7500 = Rs 1875
- Profit on Y at 35% = 0.35 × 7500 = Rs 2625
- Difference = 2625 - 1875 = Rs 750 ✓

This confirms our answer. The cost price of item X is Rs 7500.