Question

There would be 10% loss if a toy is sold at Rs. 10.80 per piece. At what price should it be sold to earn a profit of 20%?
(A) Rs. 12
(B) Rs. 12.96
(C) Rs. 14.40
(D) None of these

Answer 1

- Hint: Assume that the cost price of the toy is Rs. x. It is given that there would be 10% loss if a toy is sold at Rs. 10.80 per piece. Use the formula, \[Selling\,price=Cost\,price-Loss\] and calculate the selling price of the toy in terms of x. Now, replace the selling price by Rs. 10.80. Then, calculate the cost price of the toy. Now, use the formula, \[\text{Selling}\,\text{price=Cost}\,\text{price+Profit}\] and get the selling price if the profit is 20% of the cost price.

Complete step-by-step solution

First of all, let us assume that the cost price of the toy is Rs. x.
The cost price of the toy = Rs. x ………………………………..(1)
It is given that there would be 10% loss if a toy is sold at Rs. 10.80 per piece.
The selling price of the toy = Rs. 10.80 …………………………………(2)
Since there is a loss of 10% so, the loss would be 10% of the cost price of the toy.
The loss by selling a toy = Rs. 10% of x …………………………..(3)
We know the formula, \[Selling\,price=Cost\,price-Loss\] ………………………..(4)
Now, from equation (1), equation (3), and equation (4), we get
\[\Rightarrow Selling\,price=Rs.x-Rs.10\%\,of\,x\]
\[\begin{align}
  & \Rightarrow \text{Selling}\,\text{price=}Rs.\left( x-10\%\,of\,x \right) \\
 & \Rightarrow \text{Selling}\,\text{price=}Rs.\left( x-\dfrac{10}{100}x \right) \\
 & \Rightarrow \text{Selling}\,\text{price=}Rs.\left( x-\dfrac{x}{10} \right) \\
 & \Rightarrow \text{Selling}\,\text{price=}Rs.\left( \dfrac{10x-x}{10} \right) \\
 & \Rightarrow \text{Selling}\,\text{price=}Rs.\dfrac{9x}{10} \\
\end{align}\]
The selling price of toy is Rs. \[\dfrac{9x}{10}\] ………………………………………(5)
From equation (2), we have the selling price of the toy.
On comparing equation (2) and equation (5), we get
\[\begin{align}
  & \Rightarrow 10.80=\dfrac{9x}{10} \\
 & \Rightarrow 10.80\times 10=9x \\
 & \Rightarrow 108=9x \\
 & \Rightarrow \dfrac{108}{9}=x \\
 & \Rightarrow 12=x \\
\end{align}\]
So, the cost price of the toy is Rs. 12 ……………………………..(6)
Now, there is a profit of 20%.
Since there is a profit of 20% so, the profit would be 20% of the cost price of the toy.
The loss by selling a toy = Rs. 20% of x …………………………….(7)
We know the formula, \[\text{Selling}\,\text{price=Cost}\,\text{price+Profit}\] ………………………………..(8)
From equation (6), equation (7), and equation (8), we get
\[\Rightarrow \text{Selling}\,\text{price=Cost}\,\text{price+Profit}\]
\[\begin{align}
  & \Rightarrow Selling\,price=Rs.12+20\,\%\,of\text{ }Rs.12 \\
 & \Rightarrow Selling\,price=Rs.12+\dfrac{20}{100}\times Rs.12 \\
 & \Rightarrow Selling\,price=Rs.\left( 12+\dfrac{240}{100} \right) \\
 & \Rightarrow Selling\,price=Rs.\left( 12+2.40 \right) \\
 & \Rightarrow Selling\,price=Rs.14.40 \\
\end{align}\]
The selling price of the toy is Rs. 14.40.
Therefore, the selling price of the toy is Rs. 14.40.
Hence, the correct option is (C).

Note: In this question, one might calculate the selling price by adding the 20% of Rs. 10.80. This is wrong. Since the profit is 20% of the cost price of the toy. So, the selling price of the toy is 20% more than the cost price of the toy.