Question

Bananas are bought at 15 for a rupee and sold at the rate of 9 for a rupee. The gain percent is,

Answer 1

Hint:To solve this problem, we will find the cost price of 1 banana from the 15 bananas and selling price of 1 banana from 9 as in the question the cost price of 15 bananas and selling price of 9 bananas is given. Further we will find the gain percent by using the expression:
\[{\rm{Gain}}\% = \dfrac{{{\rm{S}}{\rm{.P}}{\rm{.}} - {\rm{C}}{\rm{.P}}.}}{{{\rm{C}}{\rm{.P}}.}}\]
Where, ${\rm{S}}{\rm{.P}}.$ is the selling price and ${\rm{C}}{\rm{.P}}.$ is the cost price.
Here $S.P. - C.P.$ gives the amount gained that is profit incurred.

Complete step-by-step solution:
Given:
Cost price of 15 bananas is ${\rm{Rs}}.1$.
Selling price of 9 bananas is ${\rm{Rs}}{\rm{.1}}$.
If cost price of 15 bananas is ${\rm{Rs}}{\rm{.1}}$ then to find cost price of 1 banana which is,
\[{\rm{C}}{\rm{.P}}{\rm{.}} = \dfrac{1}{{15}}\]
If selling price of 9 bananas is ${\rm{Rs}}{\rm{.1}}$ then to find selling price of 1 banana which is,
\[{\rm{S}}{\rm{.P}}{\rm{.}} = \dfrac{1}{9}\]
Now, the gain percent can be expressed as:
\[{\rm{Gain}}\% = \dfrac{{{\rm{S}}{\rm{.P}}{\rm{.}} - {\rm{C}}{\rm{.P}}.}}{{{\rm{C}}{\rm{.P}}.}}\]
Where, $S.P.$ is the selling price and $C.P.$ is the cost price.
Now, we will substitute \[{\rm{Rs}}.\dfrac{1}{{15}}\]for ${\rm{C}}{\rm{.P}}.$ and \[{\rm{Rs}}.\dfrac{1}{9}\] for ${\rm{S}}{\rm{.P}}{\rm{.}}$ in the above expression to find the gain percentage.
$
\Rightarrow{\rm{Gain}}\% = \dfrac{{{\rm{Rs}}{\rm{.}}\dfrac{1}{9} -
 {\rm{Rs}}{\rm{.}}\dfrac{1}{{15}}}}{{{\rm{Rs}}{\rm{.}}\dfrac{1}{{15}}}}\\
\Rightarrow{\rm{Gain}}\% = \dfrac{{\dfrac{{15 - 9}}{{15 \times 9}}}}{{\dfrac{1}{{15}}}}\\
\Rightarrow{\rm{Gain}}\% = \dfrac{6}{{15 \times 9}} \times \dfrac{{15}}{1}\\
\Rightarrow{\rm{Gain}}\% = \dfrac{6}{9}\\
{\rm{Gain}}\% = 66.67\%
$
The gain percent for selling bananas is $66.67\% $.

Note: In the question, the selling price is given of 9 bananas and the cost price is given of 15 bananas. Make sure to find the selling and cost price for 1 banana to solve the question. We can also solve this problem by first finding the profit separately by subtracting the cost price of banana from the selling price of one banana and then substitute it with the formula of gain percentage in which gain percentage is given by profit divided by cost price.