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# The CP of a radio is Rs. 1000 and it was sold for 800. Find loss $\%$?A) $20\%$ B) $30\%$ C) $15\%$ D) None

Last updated date: 13th Sep 2024
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Hint:
Here, we will find the percentage of loss. First, we will find the amount of loss by subtracting the selling price from the cost price. Then by using the percentage of loss formula, we will find the percentage of loss. A loss of an amount occurs if an item is sold at a lesser price than the cost of an item.

Formula Used:
We will use the following formula:
1) Amount of Loss is given by the formula ${\rm{Loss}} = C.P. - S.P.$
2) Percentage of loss Is given by the formula Loss percentage $= \dfrac{{{\rm{Loss}}}}{{C.P.}} \times 100$ , where $C.P$ and $S.P$ is the cost price and selling price respectively.

Complete step by step solution:
Complete Step by Step Solution:
We are given the cost price of a radio is Rs. 1000 and the selling price of a radio is Rs.800.
Amount of loss is obtained by subtracting the selling price from the cost price.
Substituting $C.P. = 1000$ and $S.P. = 800$ in the formula ${\rm{Loss}} = C.P. - S.P.$, we get
${\rm{Loss}} = 1000 - 800$
$\Rightarrow {\rm{Loss}} = 200$
Now, we will find the percentage of loss by dividing amount of loss by the cost price multiplied by 100.
Substituting ${\rm{Loss}} = 200$ and $C.P. = 1000$in the formula Loss percentage $= \dfrac{{{\rm{Loss}}}}{{C.P.}} \times 100$, we get
Loss percentage $= \dfrac{{200}}{{1000}} \times 100$
Simplifying the expression, we get
$\Rightarrow$ Loss percentage $= 20\%$
Therefore, the percentage of loss is $20\%$.

Thus Option (A) is the correct answer.

Note:
We know that the cost price of an item is the price of an item when it is bought. The selling price of an item is the price of an item when it is sold. If the cost price of an item is greater than the selling price of an item, then there is a loss. Similarly, if the selling price of an item is greater than the cost price of an item, then there is a profit. We should remember that the percentage of loss should be calculated only after calculating the amount of loss. The percentage value should always be calculated in terms of cost price.