Question

Mr. A sells a bicycle to Mr. B at a profit of \[20\% \] and Mr. B sells it to Mr. C at profit of \[25\% \]. If Mr. C pays Rs 1500, what did Mr. A pay for it?

Answer 1

Hint: Here we will use the logic that the selling price for Mr. A becomes the cost price of Mr. B and the selling price for Mr. B becomes the cost price of Mr. C. We will first find the price at which Mr. A sells the bicycle. Using this we will find the price at which Mr. B sells the bicycle to Mr. C. We will then equate it to the given cost price and solve it further to get the required answer.

Formula Used:
The formula of selling price is given by \[S.P = C.P\left( {\dfrac{{100 + P\% }}{{100}}} \right)\], where \[P\] is the profit, \[S.P\] is the selling price and \[C.P\] is the cost price.

Complete step-by-step answer:
Here we need to find the cost price of a bicycle for Mr. A.
Let the cost price of a bicycle for Mr. A be \[x\] .
As it is given that Mr. A sells a bicycle to Mr. B at a profit of \[20\% \]. So, we will find the selling price of a bicycle for Mr. A .
Substituting \[P = 20\% \] in the formula \[S.P = C.P\left( {\dfrac{{100 + P\% }}{{100}}} \right)\], we get
\[S.P = x\left( {\dfrac{{100 + 20}}{{100}}} \right)\]
On adding the number in the numerator, we get
\[ \Rightarrow S.P = x\left( {\dfrac{{120}}{{100}}} \right)\]
On further simplifying the terms, we get
\[ \Rightarrow S.P = \dfrac{{6x}}{5}\] ……….. \[\left( 2 \right)\]
We have calculated the selling price of the bicycle for Mr. \[A\]. So this will become the cost price for Mr. \[B\] i.e. the cost price for Mr. \[B\] will be equal to \[\dfrac{{6x}}{5}\] and it is given that Mr. \[B\] sells it to Mr. \[C\] at profit of \[25\% \] .
Substituting \[P = 25\% \] and \[CP = \dfrac{{6x}}{5}\] in the formula \[S.P = C.P\left( {\dfrac{{100 + P\% }}{{100}}} \right)\], we get

\[S.P = \dfrac{{6x}}{5}\left( {\dfrac{{100 + 25}}{{100}}} \right)\]
On adding the number in the numerator, we get
\[ \Rightarrow S.P = \dfrac{{6x}}{5} \times \left( {\dfrac{{125}}{{100}}} \right)\]
On multiplying the terms, we get
\[ \Rightarrow S.P = \dfrac{{3x}}{2}\]
We have calculated the selling price of the bicycle for Mr. \[B\]. So this will become the cost price for Mr. \[C\] i.e. the cost price for Mr. \[C\] will be equal to \[\dfrac{{3x}}{2}\].
It is given that Mr. \[C\] pays Rs 1,500 for the bicycle i.e. the cost price of bicycle for Mr. \[C\] is equal to Rs 1,500.
Equating both the cost price, we get
\[\dfrac{{3x}}{2} = 1500\]
On cross multiplying the terms, we get
\[\begin{array}{l} \Rightarrow 3x = 2 \times 1500\\ \Rightarrow 3x = 3000\end{array}\]
Now, we will divide both sides by 3. So, we get
\[\begin{array}{l} \Rightarrow \dfrac{{3x}}{3} = \dfrac{{3000}}{3}\\ \Rightarrow x = 1000\end{array}\]
Hence, the required value of the cost price of a bicycle for Mr. \[A\] is equal to Rs 1000.

Note: Here, we need to remember that we have to put only the numerical value of the profit percent and not the percentage because 100 is already used in the formula.
Here, we have found out the cost price of the bicycle. Cost price is the price at which an object is purchased. Selling price is the price at which an object is sold. If the cost price is greater than selling price then there is loss, but when the selling price is greater than the cost price, there is profit.