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A coal merchant makes a profit of \[20\% \] by selling firewood at \[25Rs\] per quintal. If he sells the firewood at \[25.50Rs\] per quintal. What is his profit percent on the whole investment?

Answer Verified Verified
Hint: When you read the question, immediately note down the selling price and cost price like parameters that are given in the question. Substitute them in the basic profit and loss related formulae to get the unknown value.

Complete step-by-step answer:
We are given with the data of profit percentage and the selling price cost.
It is given that,
A coal merchant makes a profit of \[20\% \] by selling firewood at \[25Rs\] per quintal.
Hence, we can conclude that,
Selling Price $SP = 25Rs$
And the profit percentage $ = 20\% $
As we know that we always calculate profit or loss in relation with the Selling Price.
So $20\% $ of profit means that he gains that percent of profit on one quintal if he sold at $25Rs$ and with Cost Price as $CP$ say.
Therefore, $\dfrac{{SP - CP}}{{CP}} = $ Profit Percentage or $\dfrac{{SP - CP}}{{CP}} \times 100 = $ Profit
We know Profit percentage is $20\% $ and the selling price is $25Rs$. Substitute these values in the above equation. We get,
$ \Rightarrow \dfrac{{25 - CP}}{{CP}} = 20\% $
Percentage means per cent that is per $100$. So, we can write $20\% $ as $\dfrac{{20}}{{100}}$.
Now the equation will become as follows:
$ \Rightarrow \dfrac{{25 - CP}}{{CP}} = \dfrac{{20}}{{100}}$
Now, we need to simplify the above equation in order to get the $CP$ value.
$ \Rightarrow \dfrac{{25 - CP}}{{CP}} = \dfrac{{20}}{{100}}$
Now, do the cross multiplication.
\[
   \Rightarrow 5 \times \left( {25 - CP} \right) = CP \\
   \Rightarrow 125 - 5CP = CP \\
 \]
In order to find out the value of $CP$, let us move all its terms to one side.
\[
   \Rightarrow 6CP = 125 \\
   \Rightarrow CP = \dfrac{{125}}{6} \\
   \Rightarrow CP = 20.83Rs \\
 \]
As per now, we got the value of Cost Price and that is $20.83Rs$.
Now, in the question we are asked about the profit percentage when the selling price is \[25.50Rs\].
So, in the above-mentioned formula, now we need to substitute $SP = 25.50$ and the Cost Price with $CP = 20.83$
\[ \Rightarrow \dfrac{{SP - CP}}{{CP}} \times 100 = \dfrac{{25.50 - 20.83}}{{20.83}} \times 100\]
                    \[ = \dfrac{{4.67}}{{20.83}} \times 100\]
Now taking the approximate division we will get the next step as follows: \[ \Rightarrow \dfrac{{SP - CP}}{{CP}} \times 100 = 0.2241 \times 100\]
     $ = 22.41$
It means when the merchant sells the firewood at \[25.50Rs\] per quintal, he will get $22.41\% $ of profit.

Note: Profit or loss will always be calculated on the cost price. If the selling price is more than the cost price, profit is seen. If the cost price is more than the selling price, loss is seen.