A man bought a dog and a cat for Rs. 6500. He sold the dog at a gain of 20% and cat at a loss of 10%, thereby gaining 2% on the whole. Then the cost of the dog is:

A man bought a dog and a cat for Rs. 6500. He sold the dog at a gain of 20% and cat at a loss of 10%, thereby gaining 2% on the whole. Then the cost of the dog is:

Explanation

Let the cost price of the dog be Rs. X

∴ the cost price of the cat = Rs. (6500 – X)

The man sold the dog at a gain of 20%

∴ Gain in selling the dog = 20% of X = 0.2X

Also, the man sold the cat at a loss of 10%

∴ loss in selling the cat = 10% of (6500 – X) = 0.1 × (6500 – X) = 650 – 0.1X

He gained 2% in the overall.

∴ Gain in overall transaction = 2% of 6500 = 130

∴ 130 = 0.2X – (650 – 0.1X)

0.3X = 130 + 650 = 780

X = 780/0.3 = 2600