### Brain Teasers

# Ages Ago My Age ...

My friend Rupesh said to me: "Five years ago, the sum of my age and my son's age was a third of five times the average of the present ages of my son and myself." If the son will be 15 years old in 5 years time, how old is Rupesh now?

### Answer

Rupesh's present age is 50 years.Let the ages of Rupesh and his son 5 years ago be R and S respectively.

The from the statement of Rupesh which states that "Five years ago, the sum of my age and my son's age was a third of five times the average of the present ages of my son and myself.", we can write

R+S = (1/3)*(5)*(R+5+S+5)/2

R+S = (5/3)* (R+S+10)/2

R+S = (5/6)*(R+S+10)

It is also given in the problem that the son will be 15 years old in 5 years time

i.e., S+10 = 15. or S = 5 years.

Substituting the value of S in the above equation we get,

R+5 = (5/6)*(R+5+10)

R+5 = (5/6)*(R+15)

6R+30 = 5R+75

R = 45 years.

This was Rupesh's age 5 years ago.

Hence his age today is 45 + 5

= 50 years.

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