Question

Jyoti and Meena run a ready made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%. They make a profit of 10%. Find the marked price of a suit which costs them Rs. 1470.

Answer 1

Hint: We will use the fact that gain is equal to selling price minus cost price, i.e. gain= S.P -C.P. To solve this question we will use the formula, $gain\%=\dfrac{gain}{C.P}\times 100$ to get the gain%. Also, the formula for calculating the discount % that is, \[discount\%=\dfrac{discount}{M.P}\times 100\]
(Where M.P. is the marked price of an article). And also the formula, Discount=M.P.-S.P.

Complete step by step answer:
Let the marked price of the suit be x.
Now, using the formula for finding the discount %, we can write the following
\[\begin{align}
  & \Rightarrow discount\%=\dfrac{discount}{M.P}\times 100 \\
 & \Rightarrow 12.5=\dfrac{discount}{x}\times 100 \\
 & \Rightarrow discount=\dfrac{x}{8} \\
\end{align}\]
Now, for finding the selling price of the suit, we can write and use the following formula which is
\[\begin{align}
  & \Rightarrow Discount=M.P.-S.P. \\
 & \Rightarrow \dfrac{x}{8}=x-S.P. \\
 & \Rightarrow \dfrac{7x}{8}=S.P. \\
\end{align}\]
Now, as we know the gain as well as the the gain%, we can write the following
 $\begin{align}
  & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\
 & \Rightarrow 10=\dfrac{gain}{1470}\times 100 \\
 & \Rightarrow Gain=Rs.147 \\
\end{align}$
Now, again, as we know the gain as well as the S.P., we can write the following
\[\begin{align}
  & \Rightarrow S.P.-C.P.=gain \\
 & \Rightarrow \dfrac{7x}{8}-1470=147 \\
 & \Rightarrow \dfrac{7x}{8}=1617 \\
 & \Rightarrow x=Rs.1848 \\
\end{align}\]

Hence, the marked price of the suit comes out to be Rs. 1848.

Note: In this question, it is very important to know all the formulas beforehand and also, the calculations should also be done very carefully as there are very high chances that the students might commit a mistake while solving the question and get a wrong solution. Some students may make mistakes and write SP instead of CP in the formula of gain percentage, so the students must remember all the formulas correctly in order to avoid any errors.