Question

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Number of road accident happend in 2014 in a particular district is 8000 .Due to road safety efforts ,Road accident are decreased by 15% then find the number of aaccident happend in 2016

Answer 1

Given,

• Initial Road Accidents = 8000
• Decrease Rate of Road Accidents = -15% (Negative due to to decrease)
• Time Period = 2 years (2014 - 2016)

To Find ,

• Number of Accidents happened in 2016  = ?

Solution :

We Know this Formula :

Number of Road Accident in year 2016 : -

$\implies \boxed{\bold{\red{Intial \ value ( 1 + \frac{R}{100} )^{n}}}}$

$\implies \bold{8000(1 - \frac{15}{100} )^{2}}$

$\implies \bold{8000( 1 - \frac{3}{20} )^{2}}$

$\implies \bold{8000(\frac{20 - 3}{20})^{2}}$

$\implies \bold{8000 \times (\frac{17}{20})^{2}}$

$\implies \bold{8000 \times \frac{289}{400}}$

$\implies \bold{20 \times 289}$

$\implies \boxed{\bold{5780}}$

Therefore,

⇒Number of Road Accidents in 2016 = 5780(Answer)

$\rule{200}2$

⊥When We Use Compound Interest Formula :

• Any question related to population which have population increase or decrease then use this Formula .
• The growth of bacteria if the rate of growth is known then this Formula Use.
• The value of items or any accident or other things , if the price or rate increase or decrease in the intermediate years then Use this Formula

$\rule{200}2$

Answer 2

AnswEr:-

Number of road accidents happened in 2016 = 5,780

$\rule{200}{1}$

Given:-

• Old number of road accident = 8000
• Decreased by 15%
• Time given = (2016 - 2014) = 2 years.

To find:-

• New number of road accidents in 2016 = ?

Solution:-

As here number of road accidents is decreasing so we will use formula of compound amount here.

But as we know real formula:-

☛ P(1 + r)ⁿ

But here,number of road accidents is decreasing so we will substract the percentage here.So formula used here:-

☛ P(1 - r)ⁿ

So here,

⇒ $\sf New\: number = 8000(1 - 15\%)^2$

⇒ $\sf New \: number = 8000(1 - \dfrac{15}{100})^2$

⇒ $\sf New \: number = 8000(1 - \dfrac{3}{20})^2$

⇒ $\sf New\:number = 8000(\dfrac{20 - 3}{20})^2$

⇒ $\sf New \: number = 8000(\dfrac{17}{20})^2$

⇒ $\sf New \: number = 8000(0.85)^2$

⇒ $\sf New\: number = 8000 \times 0.7225$

⇒ ${\underline{\boxed{\rm{\red{New \: number = 5780 }}}}}$

Therefore,

New number of road accidents happened in 2016 = 5,780 .