Question

Maithili purchased a Walkman from her friend. She then sold it for Rs. 90. Had it been sold for Rs. 105, the gain would have been $ \dfrac{1}{4}th $ of the former loss. What is the cost of the Walkman?

Answer 1

Hint: We first try to assume the cost of the Walkman as a variable. Then we find the amount of loss and profit for the selling prices of 90 and 105 respectively. we form the mathematical expression and solve it to find the solution of the problem.

Complete step-by-step answer:
Let the cost of the Walkman be Rs. $ x $ .
Maithili sold it for Rs. 90. She lost Rs. $ \left( x-90 \right) $ .
Had it been sold for Rs. 105, the gain would have been $ \dfrac{1}{4}th $ of the former loss.
If the selling price was 105 then the profit would have been $ \left( 105-x \right) $ .
We now mathematically express the term the gain $ \left( 105-x \right) $ would have been $ \dfrac{1}{4}th $ of the former loss of $ \left( x-90 \right) $ .
So, $ \left( 105-x \right)=\dfrac{\left( x-90 \right)}{4} $ .
We now need to simplify the equation to find the variable.
We multiply with 4 and get $ 4\left( 105-x \right)=\left( x-90 \right) $ .
So, $ 420-4x=x-90 $ .
Simplifying we get
 $ \begin{align}
  & 420-4x=x-90 \\
 & \Rightarrow 4x+x=420+90 \\
 & \Rightarrow 5x=510 \\
\end{align} $
We now divide with 5 to get
 $ \begin{align}
  & \dfrac{5x}{5}=\dfrac{510}{5} \\
 & \Rightarrow x=102 \\
\end{align} $
The cost of the Walkman is Rs. 102.
So, the correct answer is “Rs. 102.”.

Note: We need to be careful about the profit and loss formulas. In case of profit, the selling price is greater than the cost price. In case of loss, the selling price is lesser than the cost price.