Question

A shopkeeper sold two fans for Rs. \[1140\] each. On one he gains \[14\%\] while on the other he loses \[5\%\]. Calculate his gain or loss percent in the whole transaction.

Answer 1

Hint: As we know that cost price (CP) for each fan is Rs. 1140, so for each fan we must find a selling price (SP) such that the shopkeeper gets a gain of 14% on one and a loss of 5% on other. We must use a very general formula for profit/loss percentage, \[\text{Profit/loss percentage=}\dfrac{\text{Profit/Loss}}{\text{Cost Price}}\]. We use this formula to find the selling price for each case, then sum up these selling prices and the profit/loss percentage must be calculated against the total CP of the fan that is 2 times the CP of each fan that results in our answer.

Complete step by step answer:
To calculate the total selling price at which total transaction is done. But firstly we must find selling price in each of the case that produced profit of 14% on one and 5% loss on the other, that will be given as \[C{{P}_{1}}\] and \[C{{P}_{2}}\]. So calculate the SPs for each case we will use one general formula given below:
\[SP=CP+P\] or \[SP=CP-L\]
Now to calculate CP for first case in which there is a net profit of 14% on CP, we use the formula given above:
 \[SP=C{{P}_{1}}+P\]
\[C{{P}_{1}}+\dfrac{14}{100}\times C{{P}_{1}}=1140\]
\[\dfrac{114}{100}\times C{{P}_{1}}=1140\]
\[C{{P}_{1}}=1000\] in rupees
 Now to calculate SP for second case in which there is a net loss of 5% on CP= Rs. 1140, we use the formula given above:
\[C{{P}_{2}}-L=SP\]
\[C{{P}_{2}}-\dfrac{5}{100}\times C{{P}_{2}}=1140\]
\[\dfrac{95}{100}\times C{{P}_{2}}=1140\]
\[C{{P}_{2}}=1200\]
As we have obtained the SPs in both the cases, we will use total CP for transaction equal to \[C{{P}_{T}}=C{{P}_{1}}+C{{P}_{2}}\] i.e. \[C{{P}_{T}}=2200\], Total SP for entire transaction = \[S{{P}_{T}}=S{{P}_{1}}+S{{P}_{2}}\] i.e. \[S{{P}_{T}}=2280\]. As we can see that total SP is greater than total CP that means there is a net profit in the entire transaction that is given as Rs. 80.
Total profit percentage of entire transaction =\[\dfrac{\text{Profit}}{\text{Total Cost}}\times 100\]
\[\dfrac{80}{2200}\times 100\]
\[\dfrac{40}{11}\%\]
\[3.63\%\]

Hence the total profit percentage is \[3.63\%\].

Note: The student must make sure he knows what profit or loss is and how to calculate its percentage wrt cost price, they should be thoroughly aware that the profit percentage is calculated on the cost price always. The common mistakes committed include incorrect substitution of profit or loss and inability to judge whether it is profit or loss.