Question

A number is increased by 40% and then decreased by 40%. Find the net increase or decrease percent.
A.16%
B.4%
C.10%
D.5%

Answer 1

Hint: Learn how to calculate the percentage of any number. Also, learn how to calculate the percentage change of any number. Use the percentage formula to find the value of the increased and decreased number then find the net change in the number.
Formula used: If any number $$a$$ is increased by $$x\mathrm{\%}$$ then the final value of the number will be, $$b={\displaystyle \frac{a(x+100)}{100}}$$ where, $$b$$ is the final value of the number $$a$$ .
If a number $$a$$ is changed to a new value $$b$$ the change in the number percentage will be, $${\displaystyle \frac{(a\sim b)}{a}}\times 100\mathrm{\%}$$

Complete step by step solution:
 Here we have given here that a number is first increased by a $$40\mathrm{\%}$$ and then decreased by $$40\mathrm{\%}$$ . Now we have to find the final increase or decrease in the original number.
Now we know that if any number $$a$$ is increased by $$x\mathrm{\%}$$ then the final value of the number is, $$b={\displaystyle \frac{a(x+100)}{100}}$$ where, $$b$$ is the final value of the number $$a$$ .
Let’s assume that the number is $$a$$ .
Now, if we increase the number by $$40\mathrm{\%}$$ , the new value of the number will be,
 $$={\displaystyle \frac{a(40+100)}{100}}$$
 $$={\displaystyle \frac{140}{100}}a$$
 $$={\displaystyle \frac{7}{5}}a$$
Now, if we decrease the new number $${\displaystyle \frac{7}{5}}a$$ by $$40\mathrm{\%}$$ , the final value of the number will be,
 $$={\displaystyle \frac{7}{5}}a({\displaystyle \frac{100-40}{100}})$$
 $$={\displaystyle \frac{7}{5}}a({\displaystyle \frac{60}{100}})$$
 $$={\displaystyle \frac{3}{5}}\times {\displaystyle \frac{7}{5}}a$$
 $$={\displaystyle \frac{21}{25}}a$$
So, we can see that the number is less than the initial value of it.
So, the change in the number is,
 $$a-{\displaystyle \frac{21}{25}}a$$
 $$={\displaystyle \frac{4}{25}}a$$
So, percentage change in the number is,
 $${\displaystyle \frac{{\displaystyle \frac{4}{25}}a}{a}}\times 100\mathrm{\%}$$
 $$={\displaystyle \frac{4}{25}}\times 100\mathrm{\%}$$
 $$=4\times 4\mathrm{\%}$$
 $$=16\mathrm{\%}$$
Hence, the net decrease percent of the number is $$16\mathrm{\%}$$
Hence, option (A) is the correct answer.
So, the correct answer is “Option A”.

Note: The change of any number is the difference between its final and initial value. The percentage change is the value of the change in fraction with respect to the initial value times $$100$$ .
Always remember that increasing and decreasing a number by the same percentage does not keep the number as it is the value of the number that always changes.