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# Monika bought an antique painting for $Rs.60000$. She spends some amount on restoring the painting. She then sold the painting for $Rs.72080$ making a profit of $6\%$. Find the amount spent on restoring the painting.

Last updated date: 21st Jun 2024
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Hint: The profit can be calculated by subtracting the expense from the income. The expense includes cost price and restoring charges. Profit percent can be calculated by dividing the profit by total expense and multiplying it by $100$.

Formula Used:
The profit percentage of a deal is given by $\dfrac{{I - E}}{E} \times 100$, where $I$ is the total income and $E$ is the total expense.

It is given that the painting is bought for $Rs.60000$.
This gives, the cost price, $CP = 60000$
Let the extra expense made by her for restoring be $x$.
So total expense, $E = CP + x = 60000 + x$
Also the selling price is given by $SP = 72080$
The profit percentage is $6\%$.
We know that the profit percentage of a deal is given by $\dfrac{{I - E}}{E} \times 100$, where $I$ is the total income and $E$ is the total expense.
Here the income consists of the selling price only.
So, $I = SP = 72080$
But expense consists of cost price and restoring charges.
So, $E = CP + x = 60000 + x$
Thus we get,
Profit percentage is given by $\dfrac{{I - E}}{E} \times 100$
Substituting we have,
$\dfrac{{72080 - (60000 + x)}}{{(60000 + x)}} \times 100 = 6$
Simplifying we get,
$\dfrac{{12080 - x}}{{60000 + x}} \times 100 = 6$
$\Rightarrow \dfrac{{1208000 - 100x}}{{60000 + x}} = 6$
Cross-multiplying we get,
$1208000 - 100x = 360000 + 6x$
This gives,
$100x + 6x = 1208000 - 360000$
$\Rightarrow 106x = 848000$
Dividing both sides by $106$ we get,
$x = \dfrac{{848000}}{{106}}$
$\Rightarrow x = 8000$

That is the amount spent on restoring the painting is $Rs.8000$.

Note:
If the item is simply bought and sold, the profit is given by subtracting the cost price from the selling price. But here an extra charge is made on expense. So we have to consider it too along with the cost price.