Question

A dishonest shopkeeper claims to sell his goods at cost price but uses a weight of 800 gm in place of the standard 1 kg weight. What is his gain percent?
A. 25%
B. 20%
C. 15%
D. None of the above.

Answer 1

Hint:In the above question, we will first assume the cost price to be Rs. 100 per kg. Then we will use the formula of gain percentage as follows, $\text{gain percentage}=\dfrac{\text{selling price}-\text{cost price}}{\text{cost price}}\times 100$.

Complete step-by-step answer:
Let us assume the cost price of the goods to be Rs. 100 per kg or Rs. 100 per 1000 gm. We have also been given that the shopkeeper claims to sell his goods at the cost price but uses a weight of 800 gm instead of the standard 1 kg weight.
So, the selling price = cost of 1 kg goods, which implies that the selling price = Rs. 100.
But the actual weight was 800 gm, so the cost price = cost of 800 gm goods.
We know that the cost of 100 gm of goods = Rs. 100.
So, the cost of 1 gm of goods $=\text{Rs}.\dfrac{100}{1000}=\text{Rs}.\dfrac{1}{10}$.
So, that means the cost price = cost of 800 gm of goods, which is $=\text{Rs}.\dfrac{1}{10}\times 800=\text{Rs}.80$.
Now, we know that the profit percentage is given as follows,
 $\begin{align}
  & \text{Gain percentage}=\dfrac{\text{selling price}-\text{cost price}}{\text{cost price}}\times 100 \\
 & \Rightarrow \text{Gain percentage}=\dfrac{100-80}{80}\times 100 \\
 & =\dfrac{20}{80}\times 100=\dfrac{1}{4}\times 100=25\% \\
\end{align}$.
Hence, we get the gain percentage as 25%.
Therefore, the correct answer is option A.

Note: One should not get confused with the selling price and the cost price and should be careful while doing the substitution of their values. Cost price is the price at which the goods are purchased and the selling price is the price at which the goods are sold.