Question

Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt for her marked at Rs. 850.

Answer 1

Hint: We will use the fact that gain is equal to selling price subtracted from cost price, i.e. gain= S.P -C.P. Using the unitary method we will find the gain percentage. 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.

Complete step by step answer:
Let the cost price of the shirt be x.
Now, using the formula for finding the discount %, we can write the following
\[\begin{align}
  & \Rightarrow discount\%=\dfrac{discount}{M.P}\times 100 \\
 & \Rightarrow 4=\dfrac{discount}{850}\times 100 \\
 & \Rightarrow discount=Rs.34 \\
\end{align}\]
Hence, the discount on the shirt is of Rs. 34.
Now, for finding the selling price of the product, we can write and use the following formula which is
\[\begin{align}
  & \Rightarrow Discount=M.P.-S.P. \\
 & \Rightarrow 34=850-S.P. \\
 & \Rightarrow Rs.\ 816=S.P. \\
\end{align}\]
Now, we know that the selling price of the shirt is Rs. 816.
Now, as we know the gain as well as the the gain%, we can write the following
 $\begin{align}
  & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\
 & \Rightarrow 20=\dfrac{gain}{x}\times 100 \\
 & \Rightarrow Gain=\dfrac{x}{5} \\
\end{align}$
Now, again, as we know the C.P. as well as the S.P., we can write the following
\[\begin{align}
  & \Rightarrow S.P.-C.P.=gain \\
 & \Rightarrow 816-x=\dfrac{x}{5} \\
 & \Rightarrow \dfrac{6x}{5}=816 \\
 & \Rightarrow x=Rs.680 \\
\end{align}\]

Hence, the cost price of the shirt is Rs. 680.

Note: In this question, it is very important to know all the formulae 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 resulting in a wrong solution. Some students may write the formula of discount as SP - MP, but this wrong and the correct formula is discount = MP - SP.