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# A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle. (in Rs.)

Last updated date: 20th Sep 2024
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Hint: We will use the formula to find the profit as, profit = S.P -C.P. Profit percentage is the amount of profit per 100 units of C.P. Using the unitary method, we will find the gain percentage. Also, we will use $gain\%=\dfrac{gain}{C.P}\times 100$ to get the gain%. Also, the formula for calculating the discount % is that,
$discount\%=\dfrac{discount}{M.P}\times 100$
(Where M.P. is the marked price of an article). One more important thing that needs to be kept in mind is that, Discount=M.P.-S.P.

\begin{align} & \Rightarrow discount\%=\dfrac{discount}{M.P}\times 100 \\ & \Rightarrow 20=\dfrac{discount}{x}\times 100 \\ & \Rightarrow discount=\dfrac{x}{5} \\ \end{align}
\begin{align} & \Rightarrow Discount=M.P.-S.P. \\ & \Rightarrow \dfrac{x}{5}=x-S.P. \\ & \Rightarrow \dfrac{4x}{5}=S.P. \\ \end{align}
\begin{align} & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\ & \Rightarrow 20=\dfrac{360}{C.P}\times 100 \\ & \Rightarrow C.P.=\dfrac{360}{20}\times 100 \\ & \Rightarrow C.P.=Rs.1800 \\ \end{align}
\begin{align} & \Rightarrow S.P.-C.P.=gain \\ & \Rightarrow \dfrac{4x}{5}-1800=360 \\ & \Rightarrow \dfrac{4x}{5}=2160 \\ & \Rightarrow x=Rs.2700 \\ \end{align}