Question

Fill in the blanks to make the statement true: If $20$ lemons are bought for $₹10$ and sold at $5$ for three rupees, then ________ in the transaction is _______ $\%$.

• A. Profit
• B. $20\%$

Answer 1

Step 1: Apply unitary method to evaluate the price of each item

Given, cost price of $20$ lemons $=₹10$

So, the cost price of $1$ lemon will be $=₹\frac{10}{20}$, i.e. $₹\frac{1}{2}$

Now, the cost price of $5$ lemons will be $=₹\frac{5}{2}$

We are also given the sale price of $5$ lemons i.e. $₹3$

As the sale price for $5$ lemons is more than the cost price of $5$ lemons, thus, a profit is made on sale.

Step 2: Evaluate the profit

We know that, $\mathrm{Profit}\left(\mathrm{P}\right)=\mathrm{Sale}\mathrm{Price}\left(\mathrm{SP}\right)-\mathrm{Cost}\mathrm{Price}\left(\mathrm{CP}\right)$

$$\begin{gathered} \Rightarrow P=SP-CP \\ \Rightarrow P=3-\frac{5}{2} \\ \Rightarrow P=\frac{6-5}{2} \\ \Rightarrow P=\frac{1}{2} \end{gathered}$$

So, the profit percentage will be $=\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100$

$$\begin{gathered} \Rightarrow \mathrm{Profit}\%=\frac{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{{\displaystyle \raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\times 100 \\ \Rightarrow \mathrm{Profit}\%=\frac{1}{5}\times 100 \\ \Rightarrow \mathrm{Profit}\%=20\% \end{gathered}$$

Hence, a profit of $20\%$ is made on sale of lemons.