Question

a number first increased by 20percent and then decreased by 20percent.What is the net increase or decrease percent

Answer 1

let the no. be x
then 20 % of it is (20/100 )× x
then first increased will be x + 0.2x= 1.2x
now take 20% of it (20/100)×1.2x = 0.24x
decreased value = (1.2-0.24)x= 0.96 x
now this value is decreased from real value
= (1-0.96)×100
=4% decrease

Answer 2

solution with concept is given
What is Successive Percentage Change?

The concept of successive percentage change deals with two or more percentage changes applied to quantity consecutively. In this case, the final change is not the simple addition of the two percentage changes (as the base changes after the first change).

Formula for Percentage Change:

Suppose a number N undergoes a percentage change of x % and then y%, the net change is:
New number = N × (1 + x/100) × (1 + y/100)
Now, (1 + x/100) × (1 + y/100) = 1 + x/100 + y/100 + xy/10000
If we say that x + y + xy/100 = z, then (1 + x/100) × (1 + y/100) = 1 + z/100
Here, z is the effective percentage change when a number is changed successively by two percentage changes.

Various cases for Percentage Change:
Both percentage changes are positive:
x and y are positive and net increase = (x+y+xy/100) %.

One percentage change is positive and the other is negative:
x is positive and y is negative, then net percentage change = (x-y-xy/100)%

Both percentage changes are negative:
x and y both are negative and imply a clear decrease= (-x-y+xy/100)%
Percentage Change involving three changes:
If value of an object/number P is successively changed by x%, y% and then z%, then final value.

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