Question

A person sold an electronic watch at Rs 96 in such a way that his percentage profit is the same as the cost price of the watch. If he sells it at twice the percentage profit of its previous percentage then find the new selling price.

Answer 1

Hint: Since in the given question states that profit % is equal to the cost price. So, first we will use this relation to find the cost price. Once we find the cost price, we will then find the profit value. As we get the profit then after doubling its value, we can simply find new profit. Lastly, we can easily find the new selling price on substituting the new profit value with the cost price which we have already found out.

Complete step-by-step answer:
We are given that, Selling price = Rs 96.
Let us assume that,
Selling price = SP
Cost price = CP
Profit price = P
Now according to question, we have
Profit % = cost price
  $\left( \dfrac{SP-CP}{CP} \right)\times 100=CP \\ $
Substituting the value of SP = Rs 96, we get
$\begin{align}
  & \Rightarrow \left( \dfrac{96-CP}{CP} \right)\times 100=CP \\
 & \Rightarrow \left( \dfrac{96-CP}{CP} \right)\times 100=CP \\
 & \Rightarrow 9600-100CP=C{{P}^{2}} \\
 & \Rightarrow C{{P}^{2}}+100CP-9600=0 \\
 & \Rightarrow C{{P}^{2}}+\left( 160-60 \right)CP-9600=0 \\
 & \\
\end{align}$
In the above equation we are using factorization. After factorization, we got two factors as 160 and 60.
\[\begin{align}
  & \Rightarrow C{{P}^{2}}+160CP-60CP-9600=0 \\
 & \Rightarrow CP(CP+160)-60(CP+160)=0 \\
 & \Rightarrow \left( CP-60 \right)\left( CP+160 \right)=0 \\
\end{align}\]
Either,
$\begin{align}
  & \Rightarrow \left( CP+160 \right)=0 \\
 & \Rightarrow CP=-160 \\
\end{align}$
Or,
$\begin{align}
  & \Rightarrow \left( CP-60 \right)=0 \\
 & \Rightarrow CP=60 \\
\end{align}$
Cost price cannot be negative so we will exclude ‘– 160’ and take the ‘+ 60’ value.
Therefore, profit = (selling price – cost price)
$\begin{align}
  & \Rightarrow P=SP-CP \\
 & \Rightarrow P=96-60 \\
 & \Rightarrow P=Rs36 \\
\end{align}$
Again the question states that New profit = twice the older profit, so we get
$\begin{align}
  & \Rightarrow {P}'=2P \\
 & \Rightarrow {P}'=2\times 36 \\
 & \Rightarrow {P}'=Rs72 \\
\end{align}$
Therefore the we get the new selling price ($S{P}'$)
$\begin{align}
  & =60+72 \\
 & =Rs132 \\
\end{align}$
Hence the new selling price is Rs 132.

Note: Since in the question given that the selling price is Rs 92, if the profit is doubled then the new selling price will also not doubled. Because here the cost price is not changing, it will remain the same. We never take the negative value for selling price or cost price.