Question

Tarun bought a T.V with 20% discount on the labelled price. Had he bought it with a 25% discount, he would have saved Rs. 500 . At what price did he buy the T.V?
(a). Rs. 5000
(b). Rs. 10000
(c). Rs. 8000
(d). Rs. 12000

Answer 1

- Hint: The given problem is related to calculation of discount. Consider the marked price of the T.V as Rs. x and the selling price of the T.V as Rs. y . Form two equations on the basis of the information given in the problem statement, solve them simultaneously to get the values of x and y.

Complete step-by-step solution -

Before proceeding with the solution, first let’s understand the concept of discount. Discount is defined as reduction in the marked price. If the marked price of an object is M.P and the selling price of the object is S.P then the discount is calculated as Discount = M.P – S.P and the percentage discount is calculated as $%D=\dfrac{M.P-S.P}{M.P}\times 100%$ .
Now, coming to the question, it is given that the T.V was bought at a discount of 20% . So, let the marked price be Rs. x and the selling price be Rs. y . So, on applying the formula of percentage discount, we get: $20=\dfrac{x-y}{x}\times 100$ .
$\Rightarrow \dfrac{20}{100}=\dfrac{x-y}{x}$
$\Rightarrow \dfrac{1}{5}=\dfrac{x-y}{x}$
$\Rightarrow x=5x-5y$
$\Rightarrow 5y=4x.....(i)$
It is also given that if it was bought at a 25% discount, it would have been Rs. 500 cheaper, i.e. the selling price would have been Rs. 500 lesser than Rs. y . So, on applying the formula of percentage discount, we get: $25=\dfrac{x-\left( y-500 \right)}{x}\times 100$
$\Rightarrow \dfrac{25}{100}=\dfrac{x-\left( y-500 \right)}{x}$
$\Rightarrow \dfrac{1}{4}=\dfrac{x-\left( y-500 \right)}{x}$
$\Rightarrow x=4x-4y+2000$
$\Rightarrow 4y=3x+2000....(ii)$
From equation $(i)$ , we have 5y = 4x .
$x=\dfrac{5}{4}y$
On substituting $\Rightarrow x=\dfrac{5}{4}y$ in equation $(ii)$ , we get: $4y=3\times \dfrac{5y}{4}+2000$ .
$\Rightarrow 16y=15y+8000$
$\Rightarrow y=Rs.8000$
Hence, the T.V was bought at Rs. 8000 . So, option C. is the correct option.

Note: Shortcut method: Let the marked price be Rs. x . At a difference of 5% in discount, there is a difference of Rs. 500 . So, 5% of x = 500.
$\Rightarrow \dfrac{x}{20}=500$
$\Rightarrow x=10000$
So, the marked price of the T.V is Rs. 10000 . The T.V is bought at a 20% discount. So, S.P = 80% of 10000 = Rs. 8000. So, the T.V is bought at Rs. 8000 .