Question

A tricycle is sold at a gain of 16%. Had it been sold for Rs 100 more, the gain would have been 20 %. Find the C.P. of the tricycle.

Answer 1

Hint: We will assume the cost price of the tricycle as Rs.x. Then, we will use the formula, $gain\%=\dfrac{gain}{C.P}\times 100$ to get the value of gain from it and then we will use the formula, gain = SP - CP and get CP from there and then again on substituting the value of gain and CP in the formula of gain% and we will get the value of x from there.

Complete step by step answer:
Let us first take the cost price(C.P.) of the tricycle to be Rs.x.
Now, it is given in the question that he sold the tricycle at a gain% of 16%.
Now, using the formula for calculating the gain that is given in the hint, we get the following
$\begin{align}
  & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\
 & \Rightarrow 16=\dfrac{gain}{x}\times 100 \\
 & \Rightarrow gain=\dfrac{16x}{100}=\dfrac{4x}{25} \\
\end{align}$
Now. Using the gain amount, we can calculate the selling price of the tricycle which is as follows
\[\begin{align}
  & \Rightarrow gain=\text{ S}.P\text{ }-C.P. \\
 & \Rightarrow \dfrac{4x}{25}=S.P.-x \\
 & \Rightarrow S.P.=\dfrac{29x}{25} \\
\end{align}\]
Now, it is given in the question that had it been sold for Rs. 100 more, the gain would have been 20%.
Now, again using the same formula for calculating the gain%, we could write as follows
$\begin{align}
  & \Rightarrow gain\%=\dfrac{gain}{C.P}\times 100 \\
 & \Rightarrow 20=\dfrac{S.P.-C.P.}{x}\times 100 \\
 & \Rightarrow 20=\dfrac{\dfrac{29x}{25}+100-x}{x}\times 100 \\
 & \Rightarrow 1=\dfrac{\dfrac{4x}{25}+100}{x}\times 5 \\
 & \Rightarrow x=\dfrac{4x}{5}+500 \\
 & \Rightarrow \dfrac{x}{5}=500 \\
 & \Rightarrow x=Rs.2500 \\
\end{align}$

Hence, the cost price of tricycle comes out as Rs. 2500.

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 and getting to a solution. Some students may write SP instead of CP in the formula of gain percentage and this will lead to the formation of wrong answers.