# Assignment On Ages

**PROBLEMS BASED ON AGES**

**Rule 1**

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Theorem: If t years earlier the father’s age was x times that of his son. At present the father’s age is y times that of his son. Then the present ages of the son and the father are

t (x – 1) t(x - 1)

—————————— and y ———————— respectively.

x – y x - y

**Rule 2**

Theorem: If the present age of the father is x time the age of his son. t years hence, the father’s age becomes y times the age of his son. Then the present ages of the father and his son are

(y – 1)t (y - 1)t

x ———————— and ———————— years respectively.

x – y x - y

**Rule 3**

Theorem: If t years earlier, the father’s age was x times that of his son. At present the father’s age is y times that of his son. Then the sum total of the age of the father and the son is

t(x – 1)

———————— (y + 1) years.

x – y

**Rule 4**

Theorem: If the present age of the father is x time that the age of his son. t years hence, the father’s age becomes y times the age of his son. Then the present sum of the present ages of the father and his son is

t(y – 1)

———————— (x + 1) years.

x – y

**SOME PROBLEMS**

The age of the father 4 years ago was 8 times the age of his son. At present the father’s age is 4 times that of his son. Find the present age of son.

The age of the father 8 years ago was 5 times the age of his son. At present the father’s age is 3 times that of his son. Find the present age of son.

The age of Mrs. Anjali is 5 times the age of his son. After 12 years the age of Mrs. Anjali will be only twice the age of his son. Find the present age of Mrs. Anjali’s son.