On selling a T.V. at 10% gain and a fridge at 5% gain, a shopkeeper gains Rs 6000. But if he sells the T.V. at 10% gain and the fridge at 5% loss. He gains Rs 1500 on the transaction. Find the actual prices of T.V. and fridge.

Let the actual price of T.V. be ‘a’ and actual price of fridge be ‘b’.

Given, on selling a T.V. at 10% gain and a fridge at 5% gain, a shopkeeper gains Rs 6000.

∴ 10% of a + 5% of b = 6000

⇒ 10a + 5b = 600000 …… (1)

Also, if he sells the T.V. at 10% gain and the fridge at 5% loss.

∴ 10% of a – 5% of b = 1500

⇒ 10a – 5b = 150000 ……(2)

Subtract eq (2) from eq (1) to get,

10a –10 a + 5b – (–5b) = 600000 – 150000

⇒ 5b + 5b = 450000

⇒ 10b = 450000

⇒ b = 45000

Put this value of b in (1) to get,

10a + 5(45000) = 600000

⇒ 10a + 225000 = 600000

⇒ 10a = 375000

a = 37500

Hence the actual price of T.V. is 37500 and actual price of fridge is 45000.