Question

Raju sold a bicycle to Amit at $8$% profit. Amit repaired it, spending rupees $54$. Then he sold the bicycle to Nikhil for rupees $1134$ with no loss and no profit. Find the cost price of the bicycle for which Raju purchased it.

Answer 1

Hint:
Consider the cost price of the bicycle for which Raju purchased $x$. We know the profit that Raju had sold because there is no loss and profit. We’ll find 8% of x because it’s the profit Raju made.

Complete step by step solution:
Cost price of the bicycle which Raju bought was $x$.
Cost price means the amount which we spend on a bicycle.
Raju sold the bicycle to Amit with the profit of $8$% which means it is $8$% above the cost price
We can say,
The selling price of the bicycle =$108$% of the cost price
 Selling price means the amount which we get when the bicycle is sold. If we convert % into number we want to divide the number by $100$
which means the selling price is $\dfrac{108x}{100}$
From that we can Amit bought it for $\dfrac{108x}{100}$
Amit spent rupees $54$ to repair this bicycle so we have to add $54$ to Amit cost price.
Cost price for Amit is$\dfrac{108x}{100}$, add $54$ to that we get,
$\Rightarrow \dfrac{108x}{100}+54$
Amit sold to Nikhil for rupees $1134$ with no loss and no profit so there is no need to add and to subtract.
So,
$\Rightarrow \dfrac{108x}{100}+54=1134$
Take $54$ to the RHS (Right Hand Side)
$\Rightarrow \dfrac{108x}{100}=1134-54$
Subtract these two numbers we get,
$\Rightarrow \dfrac{108x}{100}=1080$
Take this $100$ to RHS
$\begin{align}
  & \Rightarrow 108x=1080\times 100 \\
 & \Rightarrow 108x=108000 \\
 & \Rightarrow x=\dfrac{108000}{108} \\
\end{align}$
Cancelling these numbers we get,
$x=1000$

Raju bought the bicycle for rupees $1000$.

Note:
From this value we can also find the cost price for Amit and Nikhil. If we are given by a cost and selling price and we need to find the profit% we have a formula that, $\dfrac{s.p-c.p}{c.p}\times 100$ whether if you need to find a loss% we have a formula that, $\dfrac{c.p-s.p}{c.p}\times 100$.