Question

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.)

Answer 1

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 $gain\mathrm{\%}={\displaystyle \frac{gain}{C.P}}\times 100$ to get the gain%. Also, the formula for calculating the discount % is that,
$$discount\mathrm{\%}={\displaystyle \frac{discount}{M.P}}\times 100$$
(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.

Complete step by step answer:
Let the marked price of the cycle be x.
Now, using the formula for finding the discount %, we can write the following
$$\begin{array}{rl}& \Rightarrow discount\mathrm{\%}={\displaystyle \frac{discount}{M.P}}\times 100\\ & \Rightarrow 20={\displaystyle \frac{discount}{x}}\times 100\\ & \Rightarrow discount={\displaystyle \frac{x}{5}}\end{array}$$
Now, for finding the selling price of the product, we can write and use the following formula which is
$$\begin{array}{rl}& \Rightarrow Discount=M.P.-S.P.\\ & \Rightarrow {\displaystyle \frac{x}{5}}=x-S.P.\\ & \Rightarrow {\displaystyle \frac{4x}{5}}=S.P.\end{array}$$
Now, as we know the gain as well as the the gain%, we can write the following
 $\begin{array}{rl}& \Rightarrow gain\mathrm{\%}={\displaystyle \frac{gain}{C.P}}\times 100\\ & \Rightarrow 20={\displaystyle \frac{360}{C.P}}\times 100\\ & \Rightarrow C.P.={\displaystyle \frac{360}{20}}\times 100\\ & \Rightarrow C.P.=Rs.1800\end{array}$
Now, again, as we know the C.P. as well as the S.P., we can write the following
$$\begin{array}{rl}& \Rightarrow S.P.-C.P.=gain\\ & \Rightarrow {\displaystyle \frac{4x}{5}}-1800=360\\ & \Rightarrow {\displaystyle \frac{4x}{5}}=2160\\ & \Rightarrow x=Rs.2700\end{array}$$

Hence, the marked price of the cycle is Rs. 2700.

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.