Question

A number of lion in a forest is proportional to square of the area of forest. in a particular year the number of lions were 1000. if after 3 years area of forest is reduced by 50%, find out the % decrease in numbers of lions.

Answer 1

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Answer 2

Answer:

Percentage decrease in number of lions is 80%

Step-by-step explanation:

Step 1: Given Data

Number of lions in the forest   is ∞ (Area of forest)^2

Assume the number of Lion taken as x

Let the Area of forest taken as y

$\mathrm{X} \propto \mathrm{Y}^{2}$

Step 2:

$\mathrm{X}=\mathrm{ky}^{2}$ [where k=1 known as constant of proportionality]

X=1000  

y= √x

Step 3:

$\begin{array}{l}{X=y^{2}} \\ {Y^{2}=1000}\end{array}$

Y= √100 x 10

Step 4:

$\mathrm{Y}=10 \sqrt{10} \mathrm{m}^{2}$,

50% reduced in $\mathrm{y}^{2}$ = 50/100 x 10 √10  

=5 √10  

Step 5: $\mathrm{y}^{2}=x$

$=(5 \sqrt{10})^{2}=x$

x=25 x 10  

Hence the number of lions is 200

Percentage decrease in number of lions = 800/1000 x 100 = 80%