A cow and a horse are bought together for Rs. 150000. The cow is sold at a…

Concept: When two items with a known combined cost price are sold at different profit and loss percentages, let the cost price of one item be x, so the other item's cost price is (Total cost price minus x). The selling price at a profit of p% is CP x (1 + p/100); at a loss of l% it is CP x (1 - l/100). The overall gain or loss equals the total selling price minus the total cost price.

1. Let the cost price of the cow be x, so the cost price of the horse is 150000 minus x.

2. The cow is sold at a 25% profit, so its selling price is 1.25x.

3. The horse is sold at a 15% loss, so its selling price is 0.85 times (150000 minus x).

4. The overall gain is Rs 5500, so total selling price equals total cost price plus overall gain: 150000 + 5500 = 155500.

5. Set up the equation: 1.25x + 0.85(150000 - x) = 155500.

6. Expand: 1.25x + 127500 - 0.85x = 155500.

7. Combine like terms: 0.4x = 155500 - 127500 = 28000.

8. Solve for x: x = 28000 / 0.4 = 70000.

Cross-check: with x = 70000, the horse's cost price is 80000. Selling price of cow = 1.25 x 70000 = 87500; selling price of horse = 0.85 x 80000 = 68000. Total selling price = 155500, which is exactly 5500 more than the total cost price of 150000, confirming the overall gain matches the question.