If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68, and if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108 What is the age of P?

Let's denote their ages as P, Q and R itself.

We are first told that If the ages of P and R are added to twice the age of Q, the total becomes 59

P+R+2Q=59----1

We are then told that the ages of Q and R are added to thrice the age of P, so the total becomes 68

Q+R+3P=68-----2

At last, we are told that the age of P is added to thrice the age of Q and thrice the age of R, so the total becomes 108

P+3Q+3R=108-----3

This is a linear equation with 3 variables, 

Multiplying the second equation with 3 we get, 
3Q+3R+9P=204

Subtracting equation 3 from this equation we get, 
8P=96
P=12

Subtracting equation 1 from 2 we get, 2P-Q=9
Q=15

Substituting this we get, R=17

Hence, P=12.