Question

Manoj's income increased by 20percet and then decreased by 20percent. What is the total percentage change in manoj's income?

Answer 1

Let the income be 100
increased by20%
= 100+ (20/100) * 100= 120
now decreased by 20%
= 120-(20/100) * 120 = 96.
so the percentage change is - 4%

Answer 2

Let the original income  be x.

Increased income = x + 20 % of x

                               = x + 20/ 100 x

                               = 120/ 100 x  = 12/10 x

Decreased  income = 12/10 x - 20% of 12/10 x

                                 = 12/10x  - 20/100 x 12/100x

                                  = 12 / 10x - 24 / 100x

                                  = 120/ 100 x - 24/ 100 x

                                   = 96/100 x

Net decrease = x/1 - 96/ 100x

                        = 100/100 x - 96/100x

                         = 4/100 x = x/25

Decrease % =x/25 /x   x   100

                    = x/25 ÷ x   x    100

                     = x/25  x  1/ x  x  100

                      = 4 %

∴ The total percent change in manoj's income is 4%