Question

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

Answer 1

HERE IS MY SOLUTION IN ATTACHMENT ⬆⬆

THERE FORE 4%IS THE TOTAL PERCENT CHANGE IN MANOJ INCOME....

TQ

Answer 2

$\huge{\underline{\bf\red{Questi {\mathbb{O}} n} :}}$

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

$\huge{\underline{\: \bf\green{Answ {\mathbb{E}} r}\ \: :}}$

The overall change in Manoj's income is $\blue{\underline{\bf\green{\quad 4 \% \quad}}}$

$\Large{\underline{\bf\purple{Giv {\mathbb{E}} n}\ :}}$

• initial increase in income = 20 %

• further decrease in income = 20 %

$\Large{\underline{\bf\purple{To \ Fi {\mathbb{N}} d}\ :}}$

• Overall increase / decrease in income

$\huge{\underline{\bf\blue{Soluti {\mathbb{O}} n}\ :}}$

Let the initial income be x rupees.

Then ,

$\begin{aligned} \sf increased \: income & = x + 20\% \: {\sf{of}} \: x \\ \\ & = x + \frac{20x}{100} \\ \\ & = \frac{100x + 20x}{100} \\ \\ & = \cancel{ \frac{120x}{100} } = \frac{6x}{5} \\ \\ & = \frac{6x}{5} & & & & & \end{aligned}$

Now, the fresh income of Manoj is of $\dfrac{6x}{5}$.

Now, the decrease percentage on new (fresh) income is of 20 % .

Thus ,

$\begin{aligned} \sf final \: income & = \frac{6x}{5} - 20\% \: {\sf{of}} \frac{6x}{5} \\ \\ & = \frac{6x}{5} - \bigg[ \frac{ \cancel{20} \ {}^{1} }{ \cancel{100} \ _{5} } \times \frac{6x}{5} \bigg] \\ \\ & = \frac{6x}{5} - \frac{6x}{25} \\ \\ & = \frac{30x - 6x}{25} \\ \\ & = \frac{24x}{25} & & & & & \end{aligned}$

We can clearly see that :

$\boxed{ \frac{24x}{25} < {\large{x}} }$

That is, the final income is less than the initial income.

Thus, the income has decreased !

Now, to get the answer, we have to calculate the decrease percentage.

$\begin{aligned} \sf total \: decrease \: \% \\ \sf of \: income \qquad & = \bigg[ \frac{x - \frac{24x}{25} }{x} \times 100 \bigg] \% \\ \\ & = \bigg[ \frac{25x - 24x}{25} \times 100\bigg]\% \\ \\ & = \bigg[ \frac{ \cancel{x}}{ _{1} \ \cancel{25} \cancel{x}} \times \cancel{100} \ {}^{4} \bigg]\% \\ \\ & = 4\% & & & & & & \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

$\purple{\rule{7.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }$