Question

Anuj bought an old sofa set and spent Rs. 1840 to put new covers on it. He sold it for Rs. 8000 at a loss of Rs. 1250. At what price did he buy the sofa set?

Answer 1

Hint: We first assume the price Anuj paid for his sofa. We know that the added value of the loss and the selling price is equal to the cost price. We find the respective values and form an equation to solve it. The solution gives the value of the cost price of the sofa.

Complete step by step solution:
Anuj bought an old sofa set and spent Rs. 1840 to put new covers on it.
Let us assume he bought the sofa for Rs. $x$.
The total money spent on the sofa is $x+1840$.
He sold it for Rs. 8000 at a loss of Rs. 1250.
As the sale was a loss, he sold it at a lesser price than the price he spent for the sofa.
We know that the added value of the loss and the selling price is equal to the cost price.
The equation gives $x+1840=8000+1250$.
We solve the equation to find the value of $x$.
\[\begin{align}
  & x+1840=8000+1250 \\
 & \Rightarrow x=9250-1840=7410 \\
\end{align}\]
Therefore, the price at which he bought the sofa is Rs. 7410.

Note:
The loss and gain is always considered with respect to the cost price. The gain happens when the selling price is greater than the cost price.