Question

The price of an article is reduced by 25% but the daily sale of the article is increased by 30%. The net effect on the daily sale receipts is
A.$2\dfrac{1}{2}\% $ decrease
B.$2\dfrac{1}{2}\% $ increase
C.2% decrease
D.2% increase

Answer 1

Hint: The product of the price of an article and daily sale is equal to the daily sale receipts. First let the price of an article be Rs. $x$ and daily sale be $y$ units. Then, use the given conditions to find the daily receipts after the price is reduced by 25% and daily sale is increased by 30%. Finally, calculate the net effect on daily sale receipt.

Complete step-by-step answer:
First of all, we will let the price of an article be Rs. $x$ and daily sale be $y$ units.
Now, we know that the product of the price of an article and daily sale is equal to the daily sale receipts.
So, we can write the daily sale receipts as $xy$.
From the given conditions, the price of an article is reduced by 25%.
Therefore, reduced price of an article becomes,
 $
  x - 25\% \left( x \right) \\
= x - \dfrac{{25}}{{100}}\left( x \right) \\
= x - \dfrac{1}{4}\left( x \right) \\
= \dfrac{3}{4}x \\
 $
Also, daily sales of the article has increased by 30%.
Therefore, increased daily sale becomes,
$
  y + 30\% \left( y \right) \\
= y + \dfrac{{30}}{{100}}\left( y \right) \\
= y + \dfrac{3}{{10}}\left( y \right) \\
= \dfrac{{13}}{{10}}y \\
$
We will now determine the new daily sale receipts by multiplying the reduced price of an article and increased daily sale.
$
   = \dfrac{3}{4}x\left( {\dfrac{{13}}{{10}}y} \right) \\
   = \dfrac{{39}}{{40}}xy \\
$
Find the change in daily sale receipts.
$\dfrac{{39}}{{40}}xy-xy = - \dfrac{{xy}}{{40}}$
Therefore, the rate of change can be calculated using the formula, $\dfrac{{{\text{change in value}}}}{{{\text{original value}}}} \times 100$
$
   = \dfrac{{ - \dfrac{{xy}}{{40}}}}{{xy}} \times 100 \\
   = - \dfrac{{100}}{{40}} \\
   = - 2\dfrac{1}{2}\% \\
$
Hence, the net effect on the daily sale receipts is $2\dfrac{1}{2}\% $ decrease.
Hence, option A is the correct one.

Note:- The rate of change can be calculated using the formula, $\dfrac{{{\text{change in value}}}}{{{\text{original value}}}} \times 100$.
The negative sign in the final answer indicates the decrease in the rate of change. Similarly, if the rate of change would have been positive it means that there is an increase in the rate of change.