Question

If a number is increased by 30% and then
decreased by 30%, the net increase/
decrease percentage will be:
(A) 9 (B) 4
(C) 16 (D) 1​

Answer 1

AnswEr :

• Let the Number be 100.
• Increase% = 30%
• Decrease% 30%

• New Number will be :

$:\implies\sf New \:Number = Old \:Number \times (100 + Increase)\% \times (100 - Decrease)\% \\\\\\:\implies\sf New\:Number = 100 \times (100 + 30)\% \times (100 - 30)\%\\\\\\:\implies\sf New\:Number = 100 \times 130\% \times 70\%\\\\\\:\implies\sf New\:Number = 100 \times\dfrac{130}{100} \times \dfrac{70}{100}\\\\\\:\implies\sf New\:Number = 13 \times 7\\\\\\:\implies\sf New\:Number = 91$

$\rule{200}{1}$

• Percentage Change in the Number :

$\longrightarrow\tt Change\% = \dfrac{Change}{Old\:Number}\times100\\\\\\\longrightarrow\tt Change\% = \dfrac{(New-Old) Number}{Old\:Number}\times100\\\\\\\longrightarrow\tt Change\% = \dfrac{(100-91)}{100}\times100\\\\\\\longrightarrow \boxed{ \red{\tt Change\% = 9\% \:Decrease}}$

⠀

∴ There will 9% Decrease in the Number.

$\rule{200}{2}$

$\boxed{\begin{minipage}{7 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\\sf New = Old \times(100+\sf Increase)\%\\ \\New=Old \times(100-Decrease\%)\end{minipage}}$

Answer 2

Answer:

Let the required number be 100

Now, according to the question.

The number is first increased by 30 %

⇒ 100 + 30 % of 100

⇒ 100 + [(30*100)/100]

⇒ 100 + 30

⇒ 130

Then, it is decreased by 30 %

⇒ 130 - (30 % of 130)

⇒ 130 - [(30*130)/100]

⇒ 130 - 39

⇒ 91

Net Decrease = 100 - 91

= 9

Percent Decrease = (Change in number*100)/100

⇒ (9*100)/100

= 9 %

Hence, the decrease percent is 9 %