18 August 2007

Puzzle:

1. Ravi is as old as Ram will be when Ravi is twice as old as Ram was when Ravi's age was half the sum of their present ages.

2. Ram is as old as Ravi was when Ram was half the age he will be 10 years from now.

How old are Ravi and Ram?

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Solution:

Ravi is 40 years old and Ram is 30 years old.


Let Ravi's age be a and let Ram's age be b.
The first sentence tells us that "Ravi is as old as Ram will be when Ravi is twice as old as Ram was when Ravi's age was half the sum of their present ages".
"Half the sum of their present ages" is: 0.5*(a+b)
So "Ravi's age was half the sum of their present ages", the following number of years ago: a - (0.5*(a+b)) = 0.5*a-0.5*b
At that moment, "Ram's age" was: b - (0.5*a-0.5*b) = 1.5*b-0.5*a.
So "twice that age" is: 3*b-a
"Ravi's age will be twice that age", in the following number of years: (3*b-a) - a = 3*b-2*a
At that moment, Ram will be: b + (3*b-2*a) = 4*b-2*a
And we are told that "that's Ravi's age", so: 3*a = 4*b.

The second sentence tells us that "Ram is as old as Ravi was when Ram was half the age he will be 10 years from now.".
"10 years from now", Ram will be: b+10
"Half that age" is: 0.5*b+5
"Ram was that age", the following number of years ago: b - (0.5*b+5) = 0.5*b-5
At that time, "Ravi was", the following number of years old: a - (0.5*b-5) = a-0.5*b+5
And that "is Ram's current age", so: b = a-0.5*b+5 or a = 1.5*b-5.

Now we have two equations:
3*a = 4*b and a = 1.5*b-5.
Solve these equations. So Ravi's age is 40, and Ram's age is 30.