Question

A number is first increased by 20% and then decreased by 20%. Find the net increase or decrease per cent.
Ans= decreased of 4%
please explain it..​

Answer 1

Solution.

☞Let us suppose the number to be $\sf\green{x}$

➝As per the first case, the number is increased by $\sf\green{ 20%}$

Hence: $\sf\green{ x + ( X × 20/100)}$

➝ $\sf\green{ X + 20x / 100}$

→$\sf\red{ lcm\: is\: 100}$

➝ $\sf\green{ 100x + 20x / 100}$

➝ $\sf\green{ 120x/100 = 6x /5 }$

☞Resultant number is $\sf\green{'6x/5}$

→As per the second case, resultant number is then decreased by $\sf\green{20%}$

☞Hence : $\sf\green{6x/5) - [(6x/5) * 20]/100}$

→Which is$\sf\green{(6x/5) - (6x/25) = 24x/25}$

☞The original number being $\sf\red{x}$, we witness a net decrease in the overall process as $\sf\green{24x / 25}$is less than $\sf\green{ x}$

☞Therefore Net decrease_

➝$\sf\green{x - (24x/25)= x/25}$

☞Net decrease in percentage= (Net Decrease/ Initial Value) × 100%

→Thus, $\sf\green{ [(x/25)/x] × 100%= 4%}$

→So, the answer is $\sf\green{ 4%}$