Question

By selling $33$ metres of cloth, one gains the selling price of $11$ metres. Find the gain percent.

Answer 1

Hint: Using the given information we can find the relation between cost price and selling price of the cloth. Then using this relation, we can find the gain percent as well. We can proceed by expressing the data in equations and then solving.

Formula used: If $CP$ is the cost price and $SP$ is the selling price of an article, then the gain is $SP - CP$.
Also, the gain percent is $\dfrac{{SP - CP}}{{CP}} \times 100$

Complete step-by-step answer:
Given that by selling $33$ metres of cloth one gains the selling price of $11$ metres.
Let the cost price of the cloth be $CP$ and the selling price be $SP$.
Then,
Cost price of $33$ metres of cloth is $33CP$.
Selling price of $33$ metres of cloth is $33SP$.
Gain/Profit of selling $33$metres is $33SP - 33CP = 33(SP - CP)$
It is said that this is equal to the selling price of $11$ metres of cloth, which is equal to $11SP$
$ \Rightarrow 33(SP - CP) = 11SP$
Opening brackets on the left-hand side we have,
$ \Rightarrow 33SP - 33CP = 11SP$
Subtracting $11SP$ from both sides,
$ \Rightarrow 33SP - 33CP - 11SP = 11SP - 11SP$
$ \Rightarrow 22SP - 33CP = 0$
which can be written as,
$22SP = 33CP$
Dividing the both sides by $22$,
$ \Rightarrow \dfrac{{22SP}}{{22}} = \dfrac{{33CP}}{{22}}$
$ \Rightarrow SP = \dfrac{{33CP}}{{22}}$
Cancelling $11$ from numerator and denominator on the right-hand side gives,
$ \Rightarrow SP = \dfrac{3}{2}CP$
Thus, we got the relation between selling price and cost price.
Now we have to find the gain percent.
Gain percent, $g = \dfrac{{SP - CP}}{{CP}} \times 100$
Substituting for $SP$ we have,
$g = \dfrac{{(\dfrac{3}{2}CP - CP)}}{{CP}} \times 100$
$ \Rightarrow g = \dfrac{{(\dfrac{3}{2} - 1)CP}}{{CP}} \times 100$
Cancelling $CP$ from numerator and denominator we have,
$g = (\dfrac{3}{2} - 1) \times 100$
$ \Rightarrow g = \dfrac{1}{2} \times 100 = 50$
That is, profit/gain percent is $50\% $
So, the answer is $50\% $.

Additional Information: If in case, the cost price is higher than the selling price, then we have a loss.
Loss $ = CP - SP$
and the loss percent $ = \dfrac{{CP - SP}}{{CP}} \times 100$

Note: Since the cost price and selling price are not given directly we used the relation between them. If they were given, then we can substitute the values and find the gain percent. Also, we can express $CP$ in terms of $SP$ instead of what we have done.