Question

Manoj's income increased by 20% and then decreased by 20%. What is the total percentage change in
Manoj's income ?​

Answer 1

Answer:

Let Manoj income be x.

Increased income =x+

100

20x

=

100

100x+20x

=

100

120x

=

5

6x

Now decreased income =

5

6x

−(

100

20

)(

5

6x

)

=

5

6x

[1−

5

1

]

=

25

24x

Change in income =x−

25

24x

=

25

x

.

% change =(

25

x

)⋅100

=

25

100⋅x

=4x%

4% of net decrease.

stay blessed ✨

Answer 2

Let's take Manoj's income as x .

$\small\orange{\underline{\overline{\tt\: Increased\:income=}}\mid}$

$x+\dfrac{20x}{100}$=$\dfrac{100x+ 20x}{100}$=$\dfrac{120x}{100}$

= $\dfrac{6x}{5}$

$\small\orange{\underline{\overline{\tt\: Decreased \:income=}}\mid}$

$\dfrac{6x}{5}$-($\dfrac{20}{100}$) ($\dfrac{6x}{5}$)

=$\dfrac{6x}{5}$[$1-\dfrac{1}{5}$ ]

= $\dfrac{24x}{25}$

$\small\orange{\underline{\overline{\tt\: Change\:in\: income=}}\mid}$

$x-\dfrac{24x}{25}$=$\dfrac{x}{25}$

$\small\orange{\underline{\overline{\tt\: Change\: percentage=}}\mid}$

$\dfrac{x}{25}.100$

=$\dfrac{100.x}{25}$

=$4x%$

$\small\red{ \underline{\underline{\sf{4x percentage \:of\: net\: decrease}}}}$