Question

Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs. 1600, find the marked price.
(a) 2000
(b) 1000
(c) 4000
(d) 8000

Answer 1

- Hint: First, we should suppose the market price is Rs. x. Then, by applying the given condition that a 20% discount is given on the marked price, we get the discounted price as $\dfrac{80x}{100}$. Then, by equating it to 1600 we can find the value of the original marked price. In this way, by solving the above equation, we can find the marked price of the pair of skates purchased by Arun at sale.


Complete step-by-step solution -
In this question, we are supposed to find the market price of an item before the discount of 20% is given over it.
Now, to get the marked price, let us suppose the market price is Rs. x.
Then, by applying the given condition that 20% discount is given on the marked price which is Rs. x.
$\dfrac{20}{100}\times x=\dfrac{20x}{100}$
Now, to get the discounted price we need to subtract the discount percent from the original marked price as:
$\begin{align}
  & x-\dfrac{20x}{100}=\dfrac{100x-20x}{100} \\
 & \Rightarrow \dfrac{80x}{100} \\
\end{align}$
So, the discounted price is $\dfrac{80x}{100}$ whose value is given in the question as Rs. 1600.
Now, by equating it to 1600 we can find the value of original marked price as:
$\begin{align}
  & \dfrac{80x}{100}=1600 \\
 & \Rightarrow x=\dfrac{1600\times 100}{80} \\
 & \Rightarrow x=2000 \\
\end{align}$
So, from the above calculation, we get the marked price as Rs. 2000.
Hence option (a) is correct.

Note: In this type of the question we should be aware of the terms marked price and discount price that marked price is always greater than discounted price. Moreover, we should also be aware that discount is offered only on marked price. So, if x% discount is offered on marled price(MP) then, the discounted price(DP) is given by:
$DP=MP-\dfrac{x}{100}\times MP$