Question

A shopkeeper bought two fans for Rs3120.He sold one of them at a profit of 36and the other at a loss of 15+.He found that each fan was sold for the same price.Find the cost price of each fan.

Answer 1

Dear student,
Let the cost price of first fan is $xRs.$
Then the cost price of second fan is $\left(3120-x\right)Rs.$
Since, profit of first fan is $36\%$.
Hence, selling price of first fan is,
$$\begin{gathered} =a+a\times \frac{36}{100} \\ =\frac{136}{100}a \end{gathered}$$
Since. loss of second fan is $15\%$.
Hence, selling price of second fan is,
$$\begin{gathered} =\left(3120-a\right)-\left(3120-a\right)\times \frac{15}{100} \\ =\frac{85}{100}\left(3120-a\right) \end{gathered}$$
According to the question, shopkeeper sold both fans on same price.
So,
$$\begin{gathered} \frac{136}{100}a=\frac{85}{100}\left(3120-a\right)\Rightarrow 136a=85\times 3120-85a \\ \Rightarrow 136a+85a=85\times 3120\Rightarrow 221a=265200 \\ \Rightarrow a=\frac{265200}{221}\Rightarrow a=1200 \end{gathered}$$
Then the cost price of first fan is $1200Rs.$ and cost price of second fan is, $3120-1200=1920Rs.$
Regards