Question

The cost of a shirt after a 15% discount is Rs. 102. What is the cost of the shirt before the discount?

Answer 1

Hint: In this type of question we have to use the concept of discount. We know that after discount the cost price gets reduced by some amount and hence we get \[SP=CP-Discount\], where \[SP-\text{ Selling Price}\] and \[CP-\text{ Cost Price}\]. In this question we consider, \[CP\] is equal to \[x\], as 15% discount is offered so we find the discount and then by using formula we obtain the required result.

Complete step by step answer:
Now, we have to find the cost price of the shirt before the 15% discount and we have given that after the discount the price of the shirt is Rs. 102.
Let us suppose that the cost price of the shirt is \[CP\] equal to \[x\]. Also we have given that after the discount price of the shirt is Rs. 102 hence, \[SP=102\].
As 15% discount is offered on the shirt, we can write,
\[\begin{align}
  & \Rightarrow \text{Discount = 15 }\!\!\%\!\!\text{ of }CP \\
 & \Rightarrow \text{Discount = }\dfrac{\text{15}}{100}\text{ }\times \text{ }x \\
 & \Rightarrow \text{Discount = }0.15x \\
\end{align}\]
As we know that,
\[\begin{align}
  & \Rightarrow SP=CP-Discount \\
 & \Rightarrow CP=SP+Discount \\
\end{align}\]
Hence, by substituting the values we get,
\[\begin{align}
  & \Rightarrow x=102+0.15x \\
 & \Rightarrow x-0.15x=102 \\
 & \Rightarrow 0.85x=102 \\
 & \Rightarrow x=\dfrac{102}{0.85} \\
 & \Rightarrow x=120 \\
\end{align}\]
Hence, the cost of the shirt before the discount is Rs. 120.

Note: One of the students can also solve this question as follows:
We know that the % discount is given by the formula,
\[\Rightarrow \%Discount=\dfrac{CP-SP}{CP}\]
Let us suppose the cost price of the shirt that is \[CP\] given by \[x\]. Also we have given that after discount price of the shirt is Rs. 102 hence, \[SP=102\] and discount offered is 15%
\[\begin{align}
  & \Rightarrow 15\%=\dfrac{x-102}{x} \\
 & \Rightarrow \dfrac{15}{100}=\dfrac{x-102}{x} \\
 & \Rightarrow 0.15=\dfrac{x-102}{x} \\
 & \Rightarrow 0.15x=x-102 \\
 & \Rightarrow x-0.15x=102 \\
 & \Rightarrow 0.85x=102 \\
 & \Rightarrow x=\dfrac{102}{0.85} \\
 & \Rightarrow x=120 \\
\end{align}\]
Hence, the cost of the shirt before the discount is Rs. 120.