The ratio of ages of P andQ in 1996 was2:3 and in 2001was7:10 what will be the ratio in 2011
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...
You can write :
y = ( x - 1896 ) / 150
like :
P / Q = ( x - 1896 ) / 150
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
To find the ratio of ages of P and Q in 2011, we need to determine the rate at which their ages are changing over the given years from 1996 to 2011. Here's how we can do it:
Step 1: Calculate the rate of change in the ratio of their ages from 1996 to 2001.
- The ratio of ages in 1996 was 2:3, and in 2001, it was 7:10.
- To find the rate of change, we need to find how much the ratio has changed in terms of the number of parts.
- From 1996 to 2001, the ratio changed by 7 - 2 = 5 parts for P and 10 - 3 = 7 parts for Q.
Step 2: Determine the rate of change per year for both P and Q.
- To find the rate of change per year, we divide the total change in parts by the number of years.
- From 1996 to 2001, there is a span of 5 years.
- So, the rate of change per year for P is 5 parts / 5 years = 1 part per year.
- Similarly, the rate of change per year for Q is 7 parts / 5 years = 1.4 parts per year.
Step 3: Calculate the change in the ratio from 2001 to 2011.
- From 2001 to 2011, there is a span of 10 years.
- For P, the change in parts would be 1 part per year x 10 years = 10 parts.
- For Q, the change in parts would be 1.4 parts per year x 10 years = 14 parts.
Step 4: Determine the ratio in 2011.
- To find the ratio in 2011, we add the change in parts to the ratio in 2001.
- The ratio in 2001 was 7:10.
- Adding 10 parts to P and 14 parts to Q, the ratio in 2011 would be 7 + 10 : 10 + 14 = 17:24.
Therefore, the ratio of ages of P and Q in 2011 would be 17:24.