A man bought a horse and a carriage for Rs. 80,000. He sold the horse at a gain of 10% and the carriage at a loss of 5%. He gained 1% on his whole transaction. What is the cost price of the horse?

Given:

Total cost price of horse and carriage = ₹80,000

Gain on horse = 10%

Loss on carriage = 5%

Overall gain = 1%

Formula used:

Let the cost price of the horse be ₹x, then the cost price of the carriage is ₹(80,000 - x).

Overall gain formula: (Total selling price - Total cost price) / Total cost price = 1%

Calculation:

Selling price of the horse = x + 10% of x = 1.1x

Selling price of the carriage = (80,000 - x) - 5% of (80,000 - x) = 0.95 × (80,000 - x)

Overall selling price = 1.1x + 0.95 × (80,000 - x)

Since overall gain is 1%:

⇒ 1.1x + 0.95 × (80,000 - x) = 80,000 + 1% of 80,000

⇒ 1.1x + 0.95 × (80,000 - x) = 80,000 + 800

⇒ 1.1x + 76,000 - 0.95x = 80,800

⇒ 0.15x = 4,800

⇒ x = 4,800 / 0.15

⇒ x = ₹32,000

∴ The cost price of the horse is ₹32,000.