Question

Articles are bought at $Rs.\,45$ per dozen and then sold at a rate of $Rs.\,85$ per score. What is the gain percent?

Answer 1

Hint: In this question, first we have to find the cost price of one article by dividing the given amount by \[12\] and the selling price of one article by dividing it by twenty. Then we have to find the gain by subtracting the cost price from the selling price and then we apply the formula of gain percent to find it.

Complete solution:
In the above question, it is given that the cost of one dozen articles is $Rs.\,45$.
We know that in one dozen there are twelve items.
Therefore, to find the cost price of one item we have to divide it by twelve.
Cost price of one article $ = \dfrac{{45}}{{12}} = Rs.3.75$
Now, the articles are sold at $Rs.\,85$ per score.
We also know that in one score there are twenty items.
Therefore, to find the selling price of one item we need to divide it by twenty.
Selling price of one article $ = \dfrac{{85}}{{20}} = Rs.4.25$
Now, we have to find the gain by subtracting the cost price from the selling price.
As such there is a gain of \[4.25 - 3.75 = Rs.0.50\;\]on each \[Rs.3.75\] (cost price).
Therefore, gain percent $ = \dfrac{{0.50}}{{3.75}} \times 100$
$ \Rightarrow \dfrac{{40}}{3} = 13.33\% $

Therefore, the gain percent is $13.33\% .$

Note:
Do not get confused in the formula of gain percent. We have to divide gain by the cost price not by selling price in order to find the gain percent. Also, in the formula we should take all the values in the same unit.