Question

On selling a T.V. at 5%gain and a fridge at 10% gain, a shopkeeper gains Rs 2000. 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.

Answer 1

Let the price of a T.V. be Rs x and that of a fridge be Rs y. Then, we have

`(5x)/100 + (10y)/100 = 2000`

=> 5x + 10y = 200000

=> 5(x + 2y) = 200000

=> x + 2y = 400000 ...(i)

And

`(10x)/100 - (5y)/100 = 1500`

`=> 10x - 5y = 150000`

`=> 5(2x - y) = 150000`

=> 2x - y = 30000

Multiplying equation (ii) by 2, we get

4x - 2y = 6000 ...(iii)

Adding equation (i) and equation (iii), we get

x + 4x = 40000 + 60000

=> 5x = 100000

=> x = 20000

Putting x = 20000 in equation (i) we get

20000 + 2y = 40000

=> 2y = 40000 - 20000

`=> y = 20000/2 = 10000`

Hence, the actual price of T.V = Rs 20, 000 and, the actual price of fridge = Rs 10, 000.