Question

a number first increases by 10% and then decrease by 10%. Find the percentage increase and decrease on the whole.​

Answer 1

Answer:

B

Step-by-step explanation:

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 = 1100×100=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.

Answer 2

Step-by-step explanation:

Let the number is increased by 10% 

x+10010x=1011x

The number is decreased by 10%

=1011x−1011x×10010

=1011x−10011x=10099x

Decrease in percentage is 

Decrease =x−10099x=100x

So, Decrease % 

=x100x×100% 

=1%

Hope it's Help you.