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.

Explanation

Let the cost price of the TV set be ₹ x and that of the fridge by ₹ y.
Then, total CP of TV and fridge = ₹ (x + y )
SP in first case = ` ₹ ((105x)/(100) + (110y)/(100)) = ₹ ((21x)/(20) + (11y)/(10)) `
` therefore ` gain in this case = ` ₹ {(( 21 x )/( 20) + (11y)/(10)) - ( x+ y )} = ₹ ((x ) /(20) + ( y) /( 10))`
So, ` (x)/( 20) + (y ) /( 10 )= 3250 rArr x + 2y = 65000" " `... (i)
SP in second case = ` ₹ ((110 x)/(100) + ( 95y)/(100)) = ₹ ((11x)/(10) + ( 19y)/( 20 )) `
` therefore ` gain in this case = ` ₹ {(( 11x )/(10) + (19y ) /(20)) - ( x+ y )} = ₹ ((x ) /(10) - (y)/(20)) `.
So, ` ( x)/(10) - (y)/(20) = 1500 rArr 2x - y = 30000" " `... (ii)
Multiplying (ii) by 2 and adding the result with (i), we get
` 5x = 60000 + 65000 rArr 5x = 125000 rArr x = 25000 `
Putting ` x = 25000` in (i) , we get
` 25000 + 2y = 65000 rArr 2y = 65000 - 25000= 40000`
`rArr y = 20000`
`therefore x = 25000 and y = 20000`
Hence, the CP of the TV set is ₹ 25000 and that of the fridge is ₹ 20000.