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.

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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.

\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}
\begin{align} & \Rightarrow Discount=M.P.-S.P. \\ & \Rightarrow \dfrac{x}{8}=x-S.P. \\ & \Rightarrow \dfrac{7x}{8}=S.P. \\ \end{align}
\begin{align} & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\ & \Rightarrow 10=\dfrac{gain}{1470}\times 100 \\ & \Rightarrow Gain=Rs.147 \\ \end{align}
\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}