Question

The ratio of ages of P andQ in 1996 was2:3 and in 2001was7:10 what will be the ratio in 2011

Answer 1

If the ratio is a linear function then :

Two point equation of straight line :

y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 )

In this case :

x1 = 1996

y1 = 2 / 3

x2 = 2001

y2 = 7 / 10


y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 )

y = 2 / 3 + [ ( 7 / 10 - 2 / 3 ) / ( 2001 - 1996 ) ] * ( x - 1996 )

y = 2 / 3 + [ [ 3 * 7 / ( 3 * 10 ) - 2 * 10 / ( 3 * 10 ) ] / ( 2001 - 1996 ) ] * ( x - 1996 )

y = 2 / 3 + [ ( 21 / 30 - 20 / 30 ) / ( 2001 - 1996 ) ] * ( x - 1996 )

y = 2 / 3 + [ ( 1 / 30 ) / 5 ] * ( x - 1996 )

y = 2 / 3 + ( 1 / 30 * 5 ) * ( x - 1996 )

y = 2 / 3 + ( 1 / 150 ) * ( x - 1996 )

y = 2 / 3 + ( x - 1996 ) / 150

y = 2 * 50 / ( 3 * 50 ) + ( x - 1996 ) / 150

y = 100 / 150 + ( x - 1996 ) / 150


y = ( x - 1996 + 100 ) / 150

y = ( x - 1896 ) / 150


The ratio in 2011 :

y = ( x - 1896 ) / 150

y = ( 2011 - 1896 ) / 150

y = 115 / 150

y = 5 * 23 / ( 5 * 30 )

y = 23 / 30

y = 0.766666...

Answer 2

You can write :

y = ( x - 1896 ) / 150

like :

P / Q = ( x - 1896 ) / 150

Answer 3

The ratio of ages of P and Q in 1996 was 2:3 and in 2001 it was7:10

What will be the ratio in 2011?

in 1996: P/Q=2/3, so Q=3P/2
in 2001: (P+5)/(Q+5)=7/10

(P+5)/(3P/2+5)=7/10
P=30
so, Q=45

In 2011, (30+15)/(45+15)=3/4