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

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Last updated date: 13th Jun 2024
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Answer
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Hint: Here we will use the logic that the selling price for A becomes the cost price for B and selling price for B becomes the cost price for C. We are given the profit percentage they made while selling, so we will use formulas for finding selling price when cost price and profit percentage are given to find the required answer. Formula for finding selling price is given by –
$SP=CP\left( \dfrac{100+P\%}{100} \right)$ , where $SP$ is the selling price, $CP$ is the cost price and $P\%$ is the profit percentage.

Complete step by step answer:
Let us suppose that the cost price of a bicycle for A be $Rs.x$. As Mr. A sells the bicycle at a profit of $20\%$, so by using the formula for finding the selling price $SP=CP\left( \dfrac{100+P\%}{100} \right)$ becomes,
$SP=x\left( \dfrac{100+20}{100} \right)$
Simplifying we get –
$SP=\left( \dfrac{120}{100} \right)x=\dfrac{6x}{5}~~~~~~~~...(1)$
We have the selling price of bicycles for A. Now this becomes the cost price of a bicycle for B. Hence, the cost price for B is $\dfrac{6x}{5}$. As Mr. B sells the bicycle to Mr. C at profit of $25\%$, so the selling price of bicycle becomes
$SP=\dfrac{6x}{5}\left( \dfrac{100+25}{100} \right)$
Simplifying we get –
$SP=\dfrac{6x}{5}\times \dfrac{125}{100}~=\dfrac{3x}{2}$
Hence, the selling price of a bicycle for B becomes $\dfrac{3x}{2}$. But we are already given a cost price for Mr. C which is $Rs.1500$. So, $\dfrac{3x}{2}$ becomes equal to $Rs.1500$.
Hence,
$\dfrac{3x}{2}=1500$
Cross multiplying, we get –
\[\begin{align}
  & 3x=1500\times 2 \\
 &\Rightarrow 3x=\dfrac{3000}{3} \\
 &\Rightarrow x=1000 \\
\end{align}\]
So, we have found that $x=Rs.1000$. Since $x$ was supposed to be the cost price of the bicycle for Mr. A.

Hence, the cost price of a bicycle for Mr. A is $Rs.1000$. Therefore, Mr. A buys the bicycle for $Rs.1000$.

Note: Students can get confused at assigning values as selling price and cost price of bicycle for different people. Students should also remember that in the formula for finding the selling price, only numeric value of the profit percentage should be used as $100$ is already present in the formula.