GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

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Question : 6 of 65

Marks: +1, -0

Population of state

{X}

increased by

{x} \%

and the population of state

{Y}

increased by

{y} \%

from 2001 to 2011 . Assume that

x

is greater than

y

. Let

P

be the ratio of the population of state

X

to state

{Y}

in a given year. The percentage increase in

{P}

from 2001 to 2011 is

$x-y$
$\;{100(x-y)}/{100+x}$
$\;{100(x-y)}/{100+y}$
$\;{x}/{y}$

Solution:

Let population of

{X}

is '

{A}

' in 2001
and Population of

Y

is 'B' in 2001

∴

Population of A in

2011= {A}(1+\;{ {x}}/{100})

& Population of

{B}

in

= {B}(1+\;{ {y}}/{100})

Given,

\;{A}/{B}=P

\%

increase in

{P}

=\;{\;{A(1+{x}/{100})}/{B(1+{y}/{100})}-{A}/{B}}/{{A}/{B}} × 100

=\;{[{P(1+{x}/{100})}/{(1+{y}/{100})}-P]}/{P} × 100

=[\;{1+{x}/{100}}/{1+\;{y}/{100}}-1] × 100=\;{(x-y) 100}/{100+y}

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