Question

A shopkeeper gains 20 % while buying the goods and 30 % while selling them. Find his total gain percentage.
A. 56 %
B. 44 %
C. 55 %
D. 50 %

Answer 1

Hint: The price at which any product is sold is the selling price of the product which is denoted by S.P and the price at which a product is bought is the cost price of the product which is denoted by C.P.

Complete Step-by-Step solution:
The formula for finding x percentage of any quantity 1 is
\[\dfrac{x}{100}\times Quantity\ 1\]
As mentioned in the question, we have to find the total gain% that the shopkeeper gets after selling the product.
Now, let the C.P or the cost price be Rs. 100.
As the shopkeeper gains 20% at the time of buying, the shopkeeper buys articles worth Rs. 120 in the price of Rs. 100.
Hence, now, we can write the selling price or the S.P of the product as follows

\[\begin{align}
  & ~S.P~=~Rs.~\dfrac{120\times (100+30)}{100}\ \\
 & S.P=~Rs.~\dfrac{120\times 130}{100}\ \\
 & S.P=~Rs.~156~ \\
\end{align}\]
Now, as the selling price or the S.P of the article is Rs. 156, so, we can write or we can calculate the %gain or the total gain% as follows
$gain=\dfrac{(156-100)}{100}\times 100=56$
Hence, the total gain% of the article or the product is 56%.

Note: The students can make an error if they don’t know the formula or the correct procedure to calculate the total gain% for the transaction and they would not be able to get to the correct answer otherwise.