Question

By selling a book for $Rs\,360$, $20\% $ profit was earned. What is the CP of the book?
A.$Rs\,300$
B.$Rs\,200$
C.$Rs\,250$
D.Cannot be determined

Answer 1

Hint: In this question we have to find the Cost price of the book. We have been given the selling price of the book i.e. SP $ = 360$ .
And we have the profit% i.e. $20\% $. So we will use the formula of CP to find this. The formula is
$CP = \dfrac{{100}}{{100 + Profit\% }} \times SP$ .
By putting the value in the formula we can get the required solution.

Complete answer: Here we have been given the selling price of the book:
 $SP = Rs\,360$
And we have the profit percentage by selling the book i.e.
$20$
We know the formula of Cost Price is
$CP = \dfrac{{100}}{{100 + Profit\% }} \times SP$ .
By putting the values in the formula we can write:
$CP = \dfrac{{100}}{{100 + 20}} \times 360$
Now we will simplify the values:
$CP = \dfrac{{100}}{{120}} \times 360$
On further solving it gives us,
$CP = 100 \times 3 \Rightarrow 300$
Hence the correct option is (A) $Rs\,300$

Note:
We can solve this question with an alternate method. We can solve this with another formula of Profit$\%$
$\dfrac{{Profit}}{{CP}} \times 100$ .
Let us assume that the percentage of profit be
$x\% $
So we can write the expression as:
Profit$\% = \dfrac{{Profit}}{{CP}} \times 100$
We can calculate the profit with the above formula:
$profit = \dfrac{{profit\% }}{{CP}} \times 100$
It can be written as:
Profit $ = $$\dfrac{x}{{100}} \times CP$
Now we know that Selling price is the sum of cost price and profit, i.e.
$SP = CP + $Profit
So by applying the above expression in this, we get:
$SP = CP + \dfrac{x}{{100}} \times CP$
Here we have profit percentage i.e.
 $x = 20$
And we have
$SP = 360$
So by using the above equation and putting the values in the formula we can write;
$360 = CP + \dfrac{{20}}{{100}} \times CP$
On further simplifying it can be written as
$360 = CP + \dfrac{{CP}}{5}$
We can take the LCM in the right hand side and add the values:
$360 = \dfrac{{5 \times CP + CP}}{5} \Rightarrow 360 = \dfrac{{6CP}}{5}$
By cross multiplication it gives the value of cost price i.e.
$CP = \dfrac{{360 \times 5}}{6} = 300$
Hence we have value of Cost price $Rs\,300$