Question

Find SP if CP = Rs.60 and loss is \[12\dfrac{1}{2}\%.\]

Answer 1

Hint: First, we will convert the loss percentage given in mixed fraction into an improper fraction. Then use the conversion rule, i.e. \[a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}.\] Now, we will apply the formula for loss percentage given by \[\text{Loss Percentage}=\dfrac{Loss}{CP}\times 100\text{ Percent,}\] where Loss = CP – SP. Then we will calculate the value of SP by substituting all the given values.

Complete step by step answer:
We have been given the cost price, CP as Rs.60 and loss % as \[12\dfrac{1}{2}\%\] and we have been asked to find out the value of SP, that is the selling price. Now, we know that the loss occurs on a product when its cost price is more than the selling price and mathematically, this loss is the difference of cost price and selling price. So, we have,
\[Loss=CP-SP\]
\[\Rightarrow Loss=60-SP.....\left( i \right)\]
Here, we have been given that the loss Percentage is \[12\dfrac{1}{2}\%.\] Let us convert this mixed fraction into an improper fraction. We know that any mixed fraction of the form \[a\dfrac{b}{c}\] can be written in improper fraction as
\[a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\]
Therefore, applying this conversion rule, we get,
\[\text{Loss Percentage}=\dfrac{\left( 12\times 2 \right)+1}{2}\%\]
\[\Rightarrow \text{Loss Percentage}=\dfrac{25}{2}\%\]
Now, applying the formula for loss percentage, we get,
\[\Rightarrow \text{Loss Percentage}=\dfrac{Loss}{CP}\times 100\%\]
\[\Rightarrow \text{Loss Percentage}=\dfrac{CP-SP}{CP}\times 100\%\]
Therefore, substituting the value of loss percentage, loss and CP, we get,
\[\Rightarrow \dfrac{25}{2}\%=\left( \dfrac{60-SP}{60} \right)\times 100\%\]
Removing the ‘%’ sign from both the sides, we get,
\[\Rightarrow \dfrac{25}{2}=\left( \dfrac{60-SP}{60} \right)\times 100\]
By cross multiplication, we get,
\[\Rightarrow 60-SP=\dfrac{25\times 60}{2\times 100}\]
Cancelling the common factors, we get,
\[\Rightarrow 60-SP=\dfrac{15}{2}\]
\[\Rightarrow 60-SP=7.5\]
\[\Rightarrow SP=60-7.5\]
\[\Rightarrow SP=Rs.52.5\]

Hence, the selling price (SP) is Rs.52.

Note: One may note that whenever there is CP greater than SP then there is loss and if SP is greater than the CP then there is profit and we calculate the profit percent. But always remember that while calculating the loss percent or profit percent, we always take CP in the denominator because loss or profit is always considered on the cost price. Also, it is necessary to convert a mixed fraction into improper fraction otherwise we will not be able to find SP.