Question

An article is sold for Rs.\[250\]at a gain of $25\% $ . Find its cost price.

Answer 1

Hint: We are given values of both selling price and gain%. Assume the cost price to be x. We can use the following formula to find the value of Cost price when selling price and Gain% are given-
S.P. =$\dfrac{{100 + {\text{gain}}\% }}{{100}} \times {\text{C}}{\text{.P}}{\text{.}}$ where S.P. is selling price and C.P. is cost price.

Complete step-by-step answer:
Given, the selling price S.P. of an article is=Rs.$250$
Gain%=$25$
We have to find the cost price C.P. of the article. Let the cost price be x.
We know the formula of selling price when gain% and C.P. is given is-
S.P. =$\dfrac{{100 + {\text{gain}}\% }}{{100}} \times {\text{C}}{\text{.P}}{\text{.}}$ where S.P. is selling price and C.P. is cost price.
Now on putting the given values in the formula we get,
S.P. =$\left( {\dfrac{{100 + 25}}{{100}}} \right) \times x$
Now on adding the values inside the bracket we get,
S.P. =$\left( {\dfrac{{125}}{{100}}} \right) \times x$
On solving the values inside the bracket we get,
S.P. =$\dfrac{5}{4}x$
Now we know that S.P. =$250$Rs. Then on putting the value of S.P. in the above equation we get,
$ \Rightarrow 250 = \dfrac{5}{4}x$
On transferring the constant numbers from right to left we get,
$ \Rightarrow 250 \times \dfrac{4}{5} = x$
We can write it as-
$ \Rightarrow $ x=$\dfrac{{250 \times 4}}{5}$
Now on solving the above equation we get,
$ \Rightarrow $ x=$50 \times 4$
On multiplying the obtained numbers, we get-
$ \Rightarrow $ x=$200$
Now we considered x to be the cost price so,
The cost price of the article=Rs.$200$.

Note: We can also directly use the formula of cost price when selling price and gain% are given which is given as-
$ \Rightarrow $ C.P. =$\dfrac{{100}}{{100 + {\text{gain% }}}} \times {\text{S}}{\text{.P}}{\text{.}}$
On putting values in the formula we get,
$ \Rightarrow $ C.P. =$\dfrac{{100}}{{100 + 25}} \times 250$
On solving the above equation we get,
$ \Rightarrow $ C.P. =$\dfrac{{25000}}{{125}}$
On division we get,
$ \Rightarrow $ C.P. =Rs.$200$