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.

Given:

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. 

To do:

We have to find the actual prices of T.V. and fridge.

Let the price of a T.V. and the price of a fridge be $x$ and $y$ respectively.

Profit on the T.V. when it is sold at a gain of 5%$=\frac{5}{100}x=0.05x$

Profit on the fridge when it is sold at a gain of 10%$=\frac{10}{100}y=0.10y$

Profit on the T.V. when it is sold at a gain of 10%$=\frac{10}{100}x=0.10x$

Loss on the fridge when it is sold at a loss of 5%$=\frac{5}{100}y=0.05y$

According to the question,

$0.05x + 0.10y = 2000$.....(i)

$0.10x - 0.05y = 1500$.....(ii)

Multiplying equation (i) by 100 on both sides, we get,

$100(0.05x+0.10y)=100(2000)$

$5x+10y=200000$

$5(x+2y)=5(40000)$

$x+2y=40000$.....(iii)

Multiplying equation (ii) by 100 on both sides, we get,

$100(0.10x-0.05y)=100(1500)$

$10x-5y=150000$

$5(2x-y)=5(30000)$

$2x-y=30000$.....(iv)

Multiplying equation (iv) by 2 on both sides, we get,

$2(2x-y)=2(30000)$

$4x-2y=60000$.....(v)

Adding equations (iii) and (v), we get,

$(x+2y)+(4x-2y)=40000+60000$

$5x=100000$

$x=\frac{100000}{5}$

$x=20000$

Substituting $x=20000$ in equation (iii), we get,

$20000+2y=40000$

$2y=40000-20000$

$2y=20000$

$y=10000$

The actual price of the T.V. is Rs. 20000 and the actual price of the fridge is Rs. 10000.   

Tutorialspoint

Updated on: 10-Oct-2022

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