Question

On selling a T.V. at 5% gain and a fridge at 10% gain, a shopkeeper gain Rs. 2000. But if he sells the T.V. at 10% gain and fridge at 5% loss, he gains Rs. 1500 on the transaction. Find the actual price of the T.V. and the fridge.

Answer 1

Let the actual price of a TV be ₹ x and actual price of a fridge be ₹ y.

A.T.Q
5% of x + 10% of y = ₹ 2000     [profit]
5x/100 + 10y/100= ₹ 2000
x/20 + y/10 = 2000
x + 2y = 2000 × 20
x + 2y = 40000……..(1)

10% of x - 5% of y = ₹ 1500      [loss]
10x/100 - 5y/100= ₹ 1500
2x/20  -  y/20= 1500
2x- y = 1500 × 20
2x  - y = 30000……..(2)

Multiply equation 1 by 2 and Subtract eq 2 .
2x + 4y = 80000
2x - y = 30000   
(-)   (+)     (-)
------------------------
5y = 50000
y = 50000/5
y = ₹ 10000

Put the value of y in eq 1
x + 2y = 40000
x +2(10000) = 40000
x + 20000 = 40000
x = 40000 - 20000
x = ₹ 20000

Hence, the actual price of TV and the fridge are ₹ 20000 and ₹ 10000.

HOPE THIS WILL HELP YOU...

Answer 2

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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