Question

A shopkeeper sells one transistor for Rs. 840 at a gain of 20 % and another for Rs. 960 at a loss of 4 %. His total gain or loss percent is which of the following:
(a) \[15\dfrac{15}{17}\%\] loss
(b) \[5\dfrac{15}{17}\%\] gain
(c) \[6\dfrac{2}{3}\%\] gain
(d) None of these

Answer 1

Hint: First find the CP of the two transistors using the formula $ CP=\left( \dfrac{100}{\left( 100+\text{profit}\% \right)}\times SP \right) $ . Add both the cost prices to get the total cost price. Add both the selling prices to get the selling price. Subtract these two to get the profit. Then use the formula Gain percent = $ \left( \dfrac{\text{Profit}}{\text{CP}}\times 100 \right)\% $ to calculate the gain percent which is our final answer.

Step-by-step answer:
In this question, we are given that a shopkeeper sells one transistor for Rs. 840 at a gain of 20 % and another for Rs. 960 at a loss of 4 %.
We need to find his total gain or loss percent.
Selling price, SP of first transistor = Rs. 840
He incurred a profit of 20 %
So, the cost price, CP of the first transistor = Rs. $ \left( \dfrac{100}{120}\times 840 \right)=700 $
Now, the Selling price, SP of second transistor = Rs. 960
He incurred a loss of 4 %
So, the cost price, CP of the second transistor = Rs. $ \left( \dfrac{100}{96}\times 960 \right)=1000 $
So, the cost price of first transistor = Rs. 700
The cost price of second transistor = Rs. 1000
Total Cost price, CP = Rs. (700 + 1000) = Rs. 1700
And, the selling price of first transistor = Rs. 840
The selling price of second transistor = Rs. 960
Total selling price, SP = Rs. (840 + 960) = Rs. 1800
Here, SP is greater than CP. So, the shopkeeper incurred a profit.
We know that Profit = SP – CP
So, Profit = Rs. (1800 – 1700) = Rs. 100
Now, we know the formula that Gain percent = $ \left( \dfrac{\text{Profit}}{\text{CP}}\times 100 \right)\% $
Using this formula, we will get the following:
Gain percent = $ \left( \dfrac{\text{100}}{\text{1700}}\times 100 \right)\%=5\dfrac{15}{17}\% $ gain.
Hence, option (b) is correct.

Note: In this question, it is very important to know the basic concepts and formulae related to profit and loss. You should know the following formulae: $ CP=\left( \dfrac{100}{\left( 100+\text{profit}\% \right)}\times SP \right) $ , Profit = SP – CP, and Gain percent = $ \left( \dfrac{\text{Profit}}{\text{CP}}\times 100 \right)\% $ . Without these, this problem will be very difficult to solve.