Question

A man buys a certain number of articles at $15$ for $Rs.112.50$ and sells them at $12$ for $Rs.108$. Find
$\left( i \right)$ His gain as a percent.
$\left( {ii} \right)$ The number of articles sold to make a profit of $Rs.75$

Answer 1

Hint:
This question can also be solved in two ways. For solving the first of all we will find the LCM of $12$ and $15$ which will become the number of articles brought. Now from this, we can easily find the cost price and similarly selling price also. So by using the formula we can find the gain percentage. Also by using the selling price we will find the number of articles needed using the unitary method.

Formula used:
Gain percentage,
$Gain\% = \dfrac{{Gain}}{{C.P}} \times 100$
$Gain = S.P - C.P$
Here,
$C.P$, will be the cost price
$S.P$, will be the selling price

Complete step by step solution:
First of all the LCM of $12$and $15$will be $60$
So the number of articles bought will be equal to $60$
Now, the cost price of the articles will be equal to
$ \Rightarrow Rs.\dfrac{{112.50}}{{15}} \times 60$
Now on solving the above, we get
$ \Rightarrow C.P = Rs.450.00$
Now the selling price of the article will be equals to
$ \Rightarrow Rs.\dfrac{{108}}{{12}} \times 60$
Now on solving the above, we get
$ \Rightarrow C.P = Rs.540.00$
So we have to find the gain percentage
Therefore by using the formula $Gain = S.P - C.P$
On substituting the values, we get
$ \Rightarrow Gain = Rs.\left( {540 - 450} \right)$
And on solving the above equation, we get
$ \Rightarrow Gain = Rs.90$
Now by using the gain percentage formula,
$Gain\% = \dfrac{{Gain}}{{C.P}} \times 100$
On substituting the values, we get
$ \Rightarrow Gain\% = \dfrac{{90}}{{450}} \times 100$
And on solving the above equation, we get
$ \Rightarrow Gain\% = 20\% $
Therefore the gain percentage will be of $20\% $
Now we will find the number of articles sold,
So as we know,
To make the profit of $Rs.90$, number of articles which are needed to be sold is equals to $Rs.60$
So by using the unitary method,
To make the profit of$\operatorname{Re} .1$, number of articles which are needed to be sold is equals to $ = \dfrac{{Rs.60}}{{Rs.90}}$
Therefore, to make the profit of$\operatorname{R} s.75$, number of articles which are needed to be sold is equals to $ \Rightarrow \dfrac{{Rs.60}}{{Rs.90}} \times 75$
And on solving the above equation, we get
$ \Rightarrow 50$

Therefore, $50$ articles needed to be sold to make the required profit.

Note:
This question can also be solved by firstly finding the C.P for one article and similarly the S.P for one article. And then we can easily find the gain and gain percentage. The rest of the process will be the same only here we don’t need to find the LCM. So it will save time too.