Question

A number is decreased by 20% and then again by 20%. by what percent should the new number be increased so as to get back the original number?

Answer 1

Let the number be 100.

Then , number is decreased by 20%.

Therefore , new number =

100 - (100 × 20/100) = 100-20 = 80

Then it is again decreased by 20%, new number =

80 - (80 × 20/100) = 80 - 16 = 64

Therefore, our new number is 64.

By what % 64 must be increased to get 100 again?

Let that % be x%

Therefore,

64 + (64 × x/100) = 100

or, 64+ (64x/100) = 100

or, 64x/100 = 100-64

or, 64x = 36×100

or, x = (36×100)/64

or, x = 56.25%

Answer → The new number must be increased by 56.25% to gain the original number back.
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