Question

On selling a fan for Rs. 810, Sam gains 8%. For how much did he purchase it?
A. 550
B. 650
C. 750
D. 850

Answer 1

Hint: We need to first assume the cost price of the fan. Using the variable and the profit of 8%, we find the selling price of the fan. Sam sold the fan at Rs. 810. This means both the terms are equal which gives us the linear equation to solve the problem. Getting the value of the variable we solve it.

Complete step by step answer:
Sam sold a fan for Rs. 810. He got gains of 8%. We need to find the price he paid to buy the fan. Let’s assume that the cost price of the fan is Rs. x.
Sam gained 8% on the price of x to sell the fan at Rs. 810.
We know the theorem of $sell=\cos t\left( 1+profit/loss \right)$
The selling price is $x\left( 1+\dfrac{8}{100} \right)=\dfrac{108x}{100}$. This price will be equal to 810.
We equate both prices to find $\dfrac{108x}{100}=810$.
We solve the linear equation to find the value of x.
$\begin{align}
  & \dfrac{108x}{100}=810 \\
 & \Rightarrow x=\dfrac{810\times 100}{108}=30\times 25=750 \\
\end{align}$
Therefore, Sam bought the fan with Rs. 750.

So, the correct answer is “Option C”.

Note: We can also use the concept of 100 where we can say when he bought the fan for 100, he sold for $100+8=108$. So, when he sold for 810 the cost price will be $\dfrac{810\times 100}{108}=30\times 25=750$. We used a unitary method to solve the problem.