Question

A man sold \[10\] eggs for \[5\] rupees and gained 20%. How many eggs did he buy for \[5\] rupees?
A) \[12\]
B) \[\dfrac{{25}}{{12}}\]
C) \[25\]
D) None of the above

Answer 1

Hint: In the above question, we are given that a man sold \[10\] eggs for the total of \[5\] rupees and made a profit of \[20\% \] . We have to find out the number of eggs that he bought for the total of \[5\] rupees. In order to approach the solution, first we have to find the selling price of one egg. After that, including the profit of \[20\% \] , we can find the cost price of one egg.

Complete step by step answer:
Given that, a man sold \[10\] eggs for \[5\] rupees and made a total profit of \[20\% \] .
We have to find the number of eggs that he bought for \[5\] rupees.
Since the selling price of \[10\] eggs is \[5\] rupees,
Hence the selling price of one egg is given by,
\[ \Rightarrow \dfrac{5}{{10}}\]
i.e.
\[ \Rightarrow 0.5\] rupees.
Now, he made a profit of \[20\% \] by selling an egg for \[0.5\] rupees.
That means each egg was bought for a cost of,
\[ \Rightarrow 0.5 \times \dfrac{{100}}{{120}}\]
That gives us,
\[ \Rightarrow \dfrac{5}{{12}}\]rupees.
Now, in \[\dfrac{5}{{12}}\] rupees, the man bought one egg,
Therefore, in \[5\] rupees, the bought must have bought the number of eggs equal to,
\[ \Rightarrow 5 \div \dfrac{5}{{12}}\]
That gives us,
\[ \Rightarrow 5 \times \dfrac{{12}}{5}\]
Hence,
\[ \Rightarrow 12\]
That is the required number of eggs which were bought for \[5\] rupees.

Therefore, the man bought a number of \[12\] eggs for \[5\] rupees. Hence, the correct option is (A).

Note:
The price at which something is bought is called the cost price or the C.P. whereas the price at which that thing is sold is called the selling price or S.P. There if profit is the S.P. is greater than the C.P. and a loss if the C.P. is greater than the S.P. Profit or loss percentage is given by the formula:
\[ \Rightarrow profit/loss\% = \dfrac{{\left| {C.P. - S.P.} \right|}}{{C.P.}} \times 100\% \]