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
