Question

A number is increased by 10% and then reduced by 10%, then the number
A. doesn’t change
B. decreases by 1%
C. increases by 1%
D. none of these

Answer 1

Hint-In this question we are given that a number is first increased by 10% and then reduced by 10%. For this, let the number at the start be 100 and apply the directions given in question to get the result.

Complete step-by-step answer:

Let the number be 100

Number is increased by 10% = 100+10% of 100

=100+10

=110

Now, the resultant number is reduced by 10% =110-10% of 110

=110-11

=99

The number obtained is 99

Decrease in value = 100 – 99 = 1

Percentage decrease = $\dfrac{1}{{100}} \times 100 = 1\% $

Hence the number is decreased by 1%.

Therefore, the correct is B.

Note- The problem can also be solved by considering the number to be x or any other unknown variable and then finding the change in the number or percentage change in terms of x. But the method of considering the number to be 100 makes the problem easier.