Question

Sugar is bought at Rs. $16.20$ per kg and sold at Rs. $17.28$ per kg. What is the gain percent?
A. $6\dfrac{2}{3}\%$
B. $3\dfrac{1}{3}\%$
C. $10\%$
D. $10\dfrac{2}{3}\%$

Answer 1

Hint: We will first analyze the question and then we will understand the meaning of profit and then to find the profit percentage of the sugar bought by the person we will apply the formula for calculating profit percent or gain percent that is: $\text{Profit }\!\!\%\!\!\text{ }=\left( \dfrac{\text{Profit}}{C.P.} \right)\times 100=\left( \dfrac{S.P.-C.P.}{C.P.} \right)\times 100$

Complete step-by-step solution:
First let’s see what is Cost Price and what is Selling Price, The amount paid to purchase an article or the price at which an article is made is known as its cost price. Cost Price is normally written as C.P. . The amount for which the product is sold is called Selling Price. It is usually denoted as SP.
Now, one makes a Profit, if the selling price (S.P.) of an article is greater than the cost price (C.P.). The difference between the selling price and cost price is called profit. Thus, if $S.P. > C.P.$, then
$\begin{align}
  & \text{Profit}=S.P.-C.P. \\
 & \text{Profit }\!\!\%\!\!\text{ }=\left( \dfrac{\text{Profit}}{C.P.} \right)\times 100=\left( \dfrac{S.P.-C.P.}{C.P.} \right)\times 100 \\
\end{align}$
For example: If a person buy some apples for Rs. $100$ and sells it for Rs. $120$ , then he has made a profit of Rs.$20\left( 120-100 \right)$ and a profit% of $20\%\left( \dfrac{20}{100}\times 100 \right)$ .
Similarly, a person is said to have a loss, if the selling price (S.P.) of an article is less than the cost price (C.P). The difference between the cost price (C.P.) and the selling price (S.P.) is called loss.
Thus, if $S.P. < C.P.$, then:
$\begin{align}
  & \text{Loss}=C.P.-S.P. \\
 & \text{Loss }\!\!\%\!\!\text{ }=\left( \dfrac{\text{Loss}}{C.P.} \right)\times 100=\left( \dfrac{C.P.-S.P.}{C.P.} \right)\times 100 \\
\end{align}$
For example: If a salesperson has bought a material for Rs. $300$ and he has to sell it for Rs.$250$ then he has gone through a loss of Rs. $50$ .

Now in the question, we have to find the gain% of the sugar, now it is given that the cost price or the amount at which sugar is purchased is Rs. $16.20$ and it is sold at Rs. $17.28$
Therefore: C.P.= $16.20$ and S.P.= $17.28$, Now as we saw above we know that :
$\begin{align}
  & \text{Profit or gain }\!\!\%\!\!\text{ }=\left( \dfrac{\text{Profit}}{C.P.} \right)\times 100=\left( \dfrac{S.P.-C.P.}{C.P.} \right)\times 100 \\
 & \Rightarrow \text{gain }\!\!\%\!\!\text{ }=\left( \dfrac{17.28-16.20}{16.20} \right)\times 100=\dfrac{1.08}{16.20}\times 100 \\
 & \Rightarrow \text{gain }\!\!\%\!\!\text{ }=\dfrac{108}{1620}\times 100=\dfrac{\dfrac{108}{108}}{\dfrac{1620}{108}}\times 100=\dfrac{1}{15}\times 100 \\
 & \Rightarrow \text{gain }\!\!\%\!\!\text{ }=\dfrac{20}{3}=6\dfrac{2}{3}\% \\
 & \Rightarrow \text{gain }\!\!\%\!\!\text{ }=6\dfrac{2}{3}\% \\
\end{align}$
Hence, the correct option is A.

Note: Note that when the profit is $m\%$ and loss is $n\%$ then the net % profit or loss will be: $\dfrac{\left( m-n-mn \right)}{100}$ . Also if a product is sold at $m\%$ and then again sold at $n\%$ profit then the actual cost price will be : $CP=\left[ \dfrac{100\times 100\times P}{\left( 100+m \right)\left( 100+n \right)} \right]$ and in case of loss: $CP=\left[ \dfrac{100\times 100\times P}{\left( 100-m \right)\left( 100-n \right)} \right]$.