Question

The price of a Maruti car rises by $30\% $ while the sales of the car come down by $20\% $. What is the percentage change in the total revenue?
A) $ - 4\% $
B) $ - 2\% $
C) $ + 4\% $
D) $ + 2\% $

Answer 1

Hint:
First, assume the initial price to be Rs. $100$ then add the increased price to the initial price to get the new price. Since it is already given that as the price increases, the sale goes down by $20\% $ so new revenue generated from the sale will be $20\% $ less of the new price. Subtract $20\% $ of the increased price from the increased price (new price). Then find the percent change by subtracting the initial revenue from the new revenue.

Complete step by step solution:
Given, the price of a Maruti car rises by $30\% $. Let the initial price of the car be Rs.$100$. This is the initial revenue of the car. Since the price of the car rise by $30\% $ then the increased price will be=initial price + the rise in the initial price
$ \Rightarrow $ The increased price=$100 + 30 = $ Rs.$130$
This is the initial
Now, it is also given that as the price increases the sales go down by $20\% $ so the revenue generated after the sale will be $20\% $ less after the increase in the price.
So the new revenue= the increased price-$20\% $ of the increased price
First, we will find $20\% $ of the increased price which can be written as-
$ \Rightarrow \dfrac{{20}}{{100}} \times 130$
On solving, we get-
$ \Rightarrow 2 \times 13 = 26$ Rs.
$ \Rightarrow $ The new revenue will be=$130 - 26$
On subtraction, we get-
The new revenue=Rs.$104$
Now, we have to find the percentage change in the total revenue.
$ \Rightarrow $ Percent change in total revenue=the new revenue- the initial revenue=$\left( {104 - 100} \right)\% $
On solving, we get-
The percentage change in the total revenue=$4\% $
Here the percentage change is positive as there is an increment in the revenue by $4\% $

Answer-The correct answer is option C.

Note:
Here the student may go wrong if they assume the increased price to be the initial revenue as initial revenue is the revenue generated from the initial price of the car. The new revenue is generated from the increased price. But since the sales go down as the price is increased, we first subtract it from the increased/new price to generate the new revenue.