Question

When the price of fans was reduced by 20% the number of fans sold increased by 40%. What was the effect on the sales rupees?
(a) 12% decrease
(b) 12% increase
(c) 30% increase
(d) 40% decrease

Answer 1

In this question, first we consider the reduced value and the increased value which is given in the question. Then we add both the values, but the reduced value must have a subtraction sign before it because it signifies decrease in the value. Now, we have to do the product of both reduced value and increased sold value and divide it by 100 to get the percentage. Subtracting both the answers we get whether sales increase or decrease. The value comes always in the percentage.

Complete step-by-step answer :
The price of fans was reduced by 20%.
The number of fans sold is increased by 40%.
Now, we add both the value, but remember the price of fans was reduced by 20% i.e. (-20) and the number of fans sold is increased by 40% i.e. (40).
$\Rightarrow \left( -20 \right)+40$.
$\therefore$ We know the basic rule of integer that “When we add one value which have subtraction sign before it and other value is positive means no sign before it or addition sign before it, in that case we subtract the expression” and always consider the sign of greater value in the answer.
$\Rightarrow 20...(1)$
The above equation (1) will be used in our result in the end.
Now,
We multiply both 20 and 40 and divide it by 100 to get the value in the percentage.
$\begin{aligned} & \Rightarrow \dfrac{20\times 40}{100} \\\ & \Rightarrow \dfrac{800}{100} \\\ & \Rightarrow 8...(2) \\\ \end{aligned}$
The above equation (2) will be useful in calculating our result for the net effect.
Now, the net effect on sales by subtracting equation (2) from equation (1):
Net Effect = 20 – 8 = 12 percent.
Therefore, the sale increased by 12 percent in rupees.
Hence, option (b) is correct.

Note :Silly mistake is bound to occur while assuming the percentage of reduction as positive. So, it must be taken care of while solving the problem. Also, the overall effect is positive so we concluded an increase in sales. If we make a mistake in sign, then we might end up with -12 percent, meaning 12% decrease. Then, we might choose option (a) as the correct answer.