Question

A number is increased by x% to get back to the original number it is to be reduced by

Answer 1

Just for ease of calculation, let us assume the number to be 100.

When x% of 100 is added to 100, we get 100+x. Now, in order to get back the original number, 100, we must reduce the current number, 100+x, by y% (say).

On applying the above logic, we get

(100+x)-y% of (100+x) = 100

[(100-y)/100]×(100+x) = 100 → (100-y)/100 = 100/(100+x) → 100-y = 10,000/(100+x)

y = 100 - [10,000/(100+x)] = (10,000+100x-10,000)/(100+x) = 100x/(100+x)