Question

If a shopkeeper sell a TV at 15% profit and a DVD at 12% loss then he earns Rs. 540 as total profit but if he sells the TV at 12% loss and the DVD at 15% profit then there is no loss or profit.Find the price of the TV and the DVD ?

Answer 1

Answer:

The price of the TV = Rs 10000

The price of the DVD = Rs 8000

Step-by-step explanation:

Let the C.P of the TV = x

Let the C.P of the DVD = y

Case 1:

Profit for the TV = 15% = (15/100) * x

Profit for the DVD = - 12% = -(12/100) * y

Profit for the TV + Profit for the DVD = 540

(15/100) * x - (12/100) * y = 540

15x - 12y = 54000  

5x - 4y = 18000     ————- Eq (1)

Case 2:

Profit for the TV = -12% = -(12/100) * x

Profit for the DVD = 15% = (15/100) * y

Profit for the TV + Profit for the DVD = 0

-(12/100) * x + (15/100) * y = 0

-12x + 15y = 0        ———- Eq (2)

Solving Eq(1) & Eq(2);

5x - 4y = 18000        x 12

-12x + 15y = 0          x 5

60x - 48y = 18000 * 12

-60x + 75y = 0

——————————-

         27y = 18000 * 12

             y = (18000 * 12)/27

             y = 8000

From Eq(2);

-12x + 15y = 0

-12x + 15(8000) = 0

12x = 15 * 2000

x = (15 * 8000)/12

x = 10000

Therefore,

The price of the TV = x = Rs 10000

The price of the DVD = y = Rs 8000

Answer 2

Hello Dear,

◆ Answer -

Price of TV = 10000 Rs

Price of DVD = 8000 Rs

◆ Explaination -

Let x and y be price of TV and DVD respectively.

Initially,

x×(15/100) + y×(-12/100) = 540

15x - 12y = 54000

5x - 4y = 18000 ...(1)

Later,

x×(-12/100) + y×(15/100) = 0

-12x + 15y = 0

15y = 12x

y = 4x/5 ...(2)

Substitute (2) in (1),

5x - 4×(4x/5) = 18000

5x - 16x/5 = 18000

9x/5 = 18000

x = 18000 × 5 / 9

x = 10000 Rs

And for y,

y = 4x/5

y = 4 × 10000 / 5

y = 8000 Rs

Therefore, price of TV is 10000 Rs and price of DVD is 8000 Rs.

Thanks dear...