Question

A man sold a fridge for Rs. 6,251 and loss is \[\dfrac{1}{20}\]of the cost price. Find the cost price.

Answer 1

Hint: We should know that if the difference between the selling price and cost price is positive, then the difference is said to be profit. If the difference between the selling price and cost price is negative, then the difference is said to be loss. So, it is clear that to obtain a loss the difference between cost price and selling price must be positive. Let us assume the cost price of fridge is equal to C.P, selling price of fridge is equal S.P and the loss obtained from fridge is equal to L. We should solve the problem with this information.

Complete step-by-step answer:
From the question, it was given that the man sold a fridge for Rs. 6,251 and lost \[\dfrac{1}{20}\] of the cost price.
So, we get
Selling price of fridge \[=Rs.6,251\]
Let us assume the selling price of fridge is equal to S.P
 \[S.P=Rs.6,251...(1)\]
Let us assume the cost price of the fridge is equal to C.P and the loss obtained from the fridge is equal to L.
We know that \[\dfrac{1}{20}\] of C.P is equal to L.
\[\Rightarrow L=\dfrac{C.P}{20}.........(2)\]
If the difference between the selling price and cost price is negative, then the difference is said to be loss.
So, to obtain a loss the difference between cost price and selling price must be positive.
Now we can write that
\[C.P-S.P=L............(3)\]
Now let us substitute equation (2) in equation (3), then we ge
 \[\begin{align}
  & \Rightarrow C.P-S.P=\dfrac{C.P}{20} \\
 & \Rightarrow 20C.P-20S.P=C.P \\
 & \Rightarrow 19C.P=20S.P \\
 & \Rightarrow C.P=\dfrac{20}{19}S.P....(4) \\
\end{align}\]
Now we will substitute equation (1) in equation (4), we get
\[\begin{align}
  & \Rightarrow C.P=\dfrac{20}{19}\left( Rs.6,251 \right) \\
 & \Rightarrow C.P=Rs.6448 \\
\end{align}\]
So, the cost of a fridge is equal to Rs.6448.

Note: This problem can be solved alternatively.
Let us assume the cost price of fridge is equal to C.P, selling price is equal to S.P and the loss obtained from fridge is equal to L.
\[S.P=Rs.6,251...(1)\]
If the difference between the selling price and cost price is negative, then the difference is said to be loss.
So, to obtain a loss the difference between cost price and selling price must be positive.
We know that \[\dfrac{1}{20}\] of C.P is equal to L.
\[\begin{align}
  & \Rightarrow L=\dfrac{C.P}{20} \\
 & \Rightarrow C.P=20L.........(2) \\
\end{align}\]
We know that if C.P is the cost price, S.P is the selling price and L is loss obtained. Then, we get
\[C.P-S.P=L............(3)\]
Now let us substitute equation (3) in equation (2), then we get
\[\begin{align}
  & \Rightarrow C.P=20(C.P-S.P) \\
 & \Rightarrow 19C.P=20S.P \\
 & \Rightarrow C.P=\dfrac{20}{19}S.P....(4) \\
\end{align}\]
Now we will substitute equation (1) in equation (4), we get
\[\begin{align}
  & \Rightarrow C.P=\dfrac{20}{19}\left( Rs.6,251 \right) \\
 & \Rightarrow C.P=Rs.6448 \\
\end{align}\]