Calculation Of The Exact Age

What was the problem? 

Let us suppose T be the age of Tommy, M be of the Mamma and P be that of Papa.

Sum of their ages is 70.

T + M + P = 70  ......(1)

and Papa is 6 times as old as Tommy,

P = 6T  .....(2)

In unknown number of years X, Papa will be twice old as Tommy,

P + X = 2 (T + X)  ....(3)

and the sum of ages at that time is 70 x 2 = 140,

(T + X) + (P + X) + (M + X) = 140.

T + P + M + 3X = 140

From (1), above equation becomes,

70 + 3X = 140

X = 70/3     .....(4)

Putting (4) and (2) in (3),

P + X = 2 (T + X) 

6T + 70/3 = 2(T + 70/3)

T = 70/12    .....(6)

Using (6) in (2),

P = 6T

P = 6(70/12)

P = 70/2    ......(7)

Putting (6) and (7) in (1),

M = 70 - 70/2 - 70/12

M = 29.1666 = 29 years 2 months.

P = 70/2 = 35 years.

T = 70/12 = 5.8333 = 5 years 10 months.

 
To summarize, the Tommy is 5 years 10 months old, Mama is 29 years 2 months old and Papa is 35 years old.