Question

A sold a watch to B at 20% gain, and B sold it to C at a loss of 10%. If C bought the watch for Rs.216, at what price did A purchase it?
A. Rs100.
B. Rs150.
C. Rs200.
D. Rs250.

Answer 1

Hint: Firstly we have to assume the CP of A and then calculate the gain with the CP by this formula \[SP=\left[ \dfrac{\left( 100+gain\% \right)}{100}\times CP \right]\]. Now we get the CP of B. Then a similar way we have to find the CP of C by using this formula \[SP=\left[ \dfrac{\left( 100-loss\% \right)}{100}\times CP \right]\]. After that we have to create an equation with the given values in the question. After calculating the equation we find the required answer.

Complete step-by-step answer:
Let us assume that the cost price (C.P) of A is x.
A sold a watch to B at 20% gain.
The formulae of selling price (S.P) for gain is,
\[SP=\left[ \dfrac{\left( 100+gain\% \right)}{100}\times CP \right]\]
Now putting the value of “gain” and C.P we get
\[\begin{align}
  & sp=\left[ \dfrac{\left( 100+20 \right)}{100}\times x \right] \\
 & \Rightarrow sp=\dfrac{120}{100}\times x \\
 & \Rightarrow sp=\dfrac{12x}{10} \\
\end{align}\]
According to the question A sold a watch to B and B sold it to C. So the S.P of A is C.P of B.
The C.P of B is \[\dfrac{12x}{10}\].
B sold it to C at a loss of 10%. The formulae of selling price (S.P) for loss is,
\[SP=\left[ \dfrac{\left( 100-loss\% \right)}{100}\times CP \right]\]
Now putting the value of “loss” and C.P we get,
\[\begin{align}
  & sp=\left[ \dfrac{\left( 100-10 \right)}{100}\times \dfrac{12x}{10} \right] \\
 & \Rightarrow sp=\dfrac{90}{100}\times \dfrac{12x}{10} \\
 & \Rightarrow sp=\dfrac{108x}{100} \\
 & \Rightarrow sp=\dfrac{27x}{25} \\
\end{align}\]
The S.P of B is C.P of C. Now C bought the watch for Rs.216. So the selling price of B is equal to the cost price of C.
Creating the equation we got,
\[\begin{align}
  & \dfrac{27x}{25}=216 \\
 & \Rightarrow x=\dfrac{216\times 25}{27} \\
 & \Rightarrow x=8\times 25 \\
 & \Rightarrow x=200 \\
\end{align}\]
The cost price (C.P) of A is Rs200 (Option C).

Note: Students has to remember the formulas of selling price in time of profit is \[SP=\left[ \dfrac{\left( 100+gain\% \right)}{100}\times CP \right]\] and in time of loss is \[SP=\left[ \dfrac{\left( 100-loss\% \right)}{100}\times CP \right]\]. If they forget then they can use \[\left( gain\% \right)=\left[ \dfrac{SP-CP}{CP}\times 100 \right]\] and rearrange it as required. They have to know how to create an equation by giving values. They also have to understand the relation between cost price and selling price.