Question

A number is first decreased by 60% and then again decreased by 80% .Find the percentage increase or decrease on the whole

Answer 1

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$\underline{\huge{\textbf{Method-1:}}}$

Let the Number be x (This will be initial value)

It is first decreased by 60% and then again decreased by 80%.

As the Number is successively decreased by a certain percentage, there will be successive percentage decrease. (i.e., percentage decrease on the whole)

$\underline{\large{\textbf{Step-1}}}$ :
Find the No. when it is decreased by 60%

New Number $N_{1}$ = x - 60% of x

$= x - ( \frac{60}{100} \times x)$

= x - 0.6x

= 0.4x

$\underline{\large{\textbf{Step-2}}}$ :
Find the No. when $N_{1}$ is decreased by 80%

New Number $N_{2}$ = 0.4x - 80% of 0.4x

$= 0.4x - ( \frac{80}{100} \times 0.4x)$

= 0.4x - (0.8×0.4x)

= 0.4x - 0.32x

= 0.08x (This is the Final Value)

$\underline{\large{\textbf{Step-3}}}$ :
Find the overall Percentage decrease

$Overall\: Percentage\: Decrease =\frac{Final\: Value-Initial\:Value}{Initial\: Value}\times100$

Overall Percentage Decrease = $\frac{x-0.08x}{x}\times100$

= $\frac{0.92x}{x}\times100$

= $92$%

Therefore,
Overall Percentage decrease = 92%

$\underline{\huge{\textbf{Method-2}}}$
Using 'STRAIGHT LINE METHOD'

$100\rightarrow60\%\downarrow\rightarrow40\rightarrow80\%\downarrow\rightarrow8$

(Here, we assume initial number as 100 and then we proceed)

Overall Percentage change = 100 - 8 = 92%

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Answer 2

\underline{\huge{\textbf{Method-1:}}}Method-1:​ 

Let the Number be x (This will be initial value)

It is first decreased by 60% and then again decreased by 80%.

As the Number is successively decreased by a certain percentage, there will be successive percentage decrease. (i.e., percentage decrease on the whole)

\underline{\large{\textbf{Step-1}}}Step-1​ :
Find the No. when it is decreased by 60% 

New Number N_{1}N1​ = x - 60% of x

= x - ( \frac{60}{100} \times x)=x−(10060​×x) 

= x - 0.6x 

= 0.4x

\underline{\large{\textbf{Step-2}}}Step-2​ :
Find the No. when N_{1}N1​ is decreased by 80% 

New Number N_{2}N2​ = 0.4x - 80% of 0.4x 

= 0.4x - ( \frac{80}{100} \times 0.4x)=0.4x−(10080​×0.4x) 

= 0.4x - (0.8×0.4x) 

= 0.4x - 0.32x 

= 0.08x (This is the Final Value)

\underline{\large{\textbf{Step-3}}}Step-3​ :
Find the overall Percentage decrease 

Overall\: Percentage\: Decrease =\frac{Final\: Value-Initial\:Value}{Initial\: Value}\times100OverallPercentageDecrease=InitialValueFinalValue−InitialValue​×100

Overall Percentage Decrease = \frac{x-0.08x}{x}\times100xx−0.08x​×100 

= \frac{0.92x}{x}\times100x0.92x​×100 

= 9292 %

Therefore, 
Overall Percentage decrease = 92% 

\underline{\huge{\textbf{Method-2}}}Method-2​ 
Using 'STRAIGHT LINE METHOD'

100\rightarrow60\%\downarrow\rightarrow40\rightarrow80\%\downarrow\rightarrow8100→60%↓→40→80%↓→8 

(Here, we assume initial number as 100 and then we proceed)

Overall Percentage change = 100 - 8 = 92%

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