Question

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On on selling a TV at 5% gain and a fridge at 10% gain A shopkeeper gains rupees 3250 but if he sells the TV at 10% gain and a fridge at 5% loss he gains rupees 1500 find the actual price of TV and that of the fridge.

And don't be oversmart. question is change from Google.​

Answer 1

Let the actual price of TV and fridge be x and y respectively

Case(i)

A shopkeeper gains rupees 3250, if he sells a TV at 5% gain and a fridge at 10% gain

ie.

$\frac{5x}{100} + \frac{10y}{100} = 3250 \\ \frac{5x + 10y}{100} = 3250 \\ 5(x + 2y) = 3250 \times 100 \\ x + 2y = \frac{3250 \times 100}{5} \\ x + 2y = 3250 \times 20 \\ x + 2y = 65000$

x+2y = 65,000 - - - - > (1)

Case(ii)

The shopkeeper will gain rupees 1500, if he sells the TV at 10% gain and a fridge at 5% loss

ie.

$\frac{10x}{100} - \frac{5y}{100} = 1500 \\ \frac{10x - 5y}{100} = 1500 \\ 5(2x - y) = 1500 \times 100 \\ 2x - y = \frac{1500 \times 100}{5} \\ 2x - y = 1500 \times 20 \\ 2x - y = 30000$

2x-y = 30,000 - - - - > (2)

Multiply eqn (1) by 2 and eqn (2) by 1

(1)x2 => 2x + 4y = 1,30,000

(2)x1 => 2x - y = 30,000

(-) (+) (-)

0 +5y = 1,00,000

5y = 1,00,000

y = 20,000

Sub y = 20,000 in eqn (1)

(1) => x+2(20,000) = 65,000

x+40,000 = 65,000

x = 65,000-40,000

x = 25,000

• Price of TV

x = ₹ 25,000

• Price of Fridge

y = ₹ 20,000