Question

15. 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 1500 on the
transaction. Find the actual prices of T.V. and fridge.​

Answer 1

Solution :-

Let the actual price of the TV be Rs. 'x' and of the fridge be Rs. 'y'.

Situation -1

By selling the TV at 5 % gain and fridge at 10 % gain, the shopkeeper gains Rs. 2000.

⇒ 5x/100 + 10y/100 = 2000

⇒ x/20 + y/10 = 2000/1

Taking the L.C.M. of the denominator and then solving it, we get.

⇒ (x + 2y)/20 = 2000

⇒ x + 2y = 40000 ...........................(1)

Situation - 2

By selling the TV at 10 % gain and fridge at 5 % loss, the shopkeeper gains Rs. 1500. The loss is indicated with the negative sign.

⇒ 10x/100 - 5y/100 = 1500

⇒ x/10 - y/20 = 1500/1

Taking the L.C.M. of the denominator and then solving it, we get.

⇒ (2x - y)/20 = 1500

⇒ 2x - y = 30000 ........................(2)

Now, multiplying the (1) by 2, and then subtracting 2 from it, we get.

First Multiplying (1) by 2 = 2*[(x + 2y) = 40000]

⇒ 2x + 4y = 80000

Now, subtracting (2) from the above.

2x + 4y = 80000

2x - y = 30000

- + -

________________

5y = 50000

__________________

⇒ 5y = 50000

⇒ y = 50000/5

⇒ y = 10000

The actual price of fridge is Rs. 10000.

Now putting the value of y = 10000 in (1), we get.

⇒ x + 2y = 40000

⇒ x + (2*10000) = 40000

⇒ x = 40000 - 20000

⇒ x = 20000

Hence, the actual price of TV is Rs. 20000 and actual price of fridge is Rs. 10000. ✔✔✔

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