On selling a T.V. at 5% gain and a fridge at 10% gain, a shopkeeper gains ₹ 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 price of the T.V. and the fridge.

#### Solution

Let the cost price of the TV be Rs “x” and the cost price of the fridge be Rs “y”.

By the given condition

`5/100 xx x + 10/100 xx y = 2000 ...["gain" = ("gain"%)/100 xx "C.P."]`

`x/20 + y/10` = 2000

Multiply by 20

x + 2y = 40000 → (1)

Again by the given second condition

`10/100 xx x - 5/100 xx y` = 1500

`x/10 - y/20` = 1500

Multiply by 20

2x – y = 30000 → (2)

(2) × 2 ⇒ 4x – 2y = 60000 → (3)

(1) + (3) ⇒ 5x + 0 = 100000

x = `100000/5`

= 20000

Substitute the value of x = 20000 in (1)

20000 + 2y = 40000

2y = 40000 – 20000

= 20000

y = `20000/2`

= 10000

Cost price of a TV = Rs 20,000

Cost price of a fridge = Rs 10,000