**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.

**Solution:**

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 T.V = Rs. $x$;

Let the S.P. of fridge $=$ Rs. $y$

S.P. of T.V at $5 \%$ gain $=\frac{5 x}{100}$

S.P. of T.V at $10 \%$ gain $=\frac{10 x}{100}$

S.P. of Fridge at $5 \%$ gain $=\frac{5 y}{100}$

S.P. of Fridge at $10 \%$ gain $=\frac{10 y}{100}$

According to the question:

$\frac{5 x}{100}+\frac{10 y}{100}=2000$

$5 x+10 y=200000$

$x+2 y=40000$

$x+2 y-40000=0$ .....(1)

$\frac{10 x}{100}-\frac{5 y}{100} y=1500$

$10 x-5 y=15000$

$2 x-1 y=30000$

$2 x-1 y=30000=0$....(2)

Hence we got the pair of equations

1*x* + 2*y* − 40000 = 0 …… (1)

2*x* − 1*y* − 30000 = 0 …… (2)

Solving the equation by cross multiplication method;

$\frac{x}{(-30000 \times 2)-(40000)}=\frac{-y}{(-30000 \times 1)-(-40000 \times 2)}=\frac{1}{(-1-4)}$

$\frac{x}{(-100000)}=\frac{-y}{(50000)}=\frac{1}{(-5)}$

$\frac{x}{(-100000)}=\frac{1}{(-5)}$

$x=20000$

$\frac{-y}{(50000)}=\frac{1}{(-5)}$

$y=10000$

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 .

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