**Tommy:** *"How old are you, Mamma?"*

**Mamma:** *"Let me think, Tommy. Well, our three ages add up to exactly ***seventy **years."

**Tommy:*** "That's a lot, isn't it? And how old are you, Papa?"*

**Papa:*** "Just six times as old as you, my son."*

**Tommy:*** "Shall I ever be half as old as you, Papa?"*

**Papa:*** "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."*

**Tommy:*** "And supposing I was born before you, Papa; and supposing Mamma had forgot all about it, and hadn't been at home when I came; and supposing..."*

**Mamma:** *"Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."*

Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the **exact age** of Mamma?

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.