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 the fridge at 5% loss. He gains Rs 1500 on the transaction. Find the actual prices of T.V. and fridge.

Answer 1

Given:

(i) On selling of a T.V. at 5% gain and a fridge at 10% gain, shopkeeper gain Rs.2000.

(ii) Selling T.V. at 10% gain and fridge at 5% loss. He gains Rs. 1500.

To find: Actual price of T.V. and fridge.

Let the S.P. of the T.V = Rs. x ; 

Let the S.P. of the Fridge = Rs. x ; 

S.P. of T.V at  5% gain `(5x)/100`

S.P. of T.V at  10% gain `(10x)/100`

S.P. of Fridge at 5% gain `(5y)/100`

S.P. of Fridge at 10% gain `(10y)/100`

According to the question:

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

`5x=10y = 200000`

`x + 2y = 40000`

`x + 2y - 40000 =0`

`(10x)/100- (5y)/100 y = 15000`

` 10 x -5y = 15000`

` 2x -1y = 30000`

`2x - 1y = 30000 = 0`

Hence we got the pair of equations

1x + 2y − 40000 = 0 …… (1)

2x − 1y − 30000 = 0 …… (2)

Solving the equation by cross multiplication method;

`x/( (-30000xx2)-(40000))= (-y)/((-30000xx1)-(-4000)) = 1/(-1-4)`

`x/(-100000)= -y/(50000)= 1/(-5)`

`x/(-100000) = 1/(-5)`

` x = 200000`

`(-y)/(50000)= 1/(-5)`

`y = 100000`

Cost of T.V. = 20000

Cost of fridge =  10000

Hence the cost of T.V. is  Rs. 20000 and that of fridge is  Rs. 10000_.