This document contains formulas and examples for solving age word problems. It provides 5 different formulas: 1) Given information about ages of a father and son in the past and present to determine their current ages. 2) Similar to Formula 1 but with information about ages in the present and future. 3) Given information about ages of a father and son in the past and future to determine their current ages. 4) Given information about the ratio of ages in the present and past to determine the current ages. 5) Given the sum of ages currently and information about ages in the future to determine the current age. Several examples are provided to demonstrate how to apply each formula to solve age

1. QA02 AGES

2. Formula 1
• 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.
• What are the present ages of the father and son?
• Father’s age =
yx
xt 1
agesSon'
yx
xyt 1
Example: The age of a man is 4 times of his son. 5 years ago,
the man was nine times as old as his son was at that time. What
is the present age of the man?
Son’s age =
49
195
= 8 years.

3. Formula 2
• The present age of father is y times the age of his son.
• After t years, the father’s age become z times the age
of his son.
• What are the present ages of the father and his son?
Son’s age =
zy
tz 1
and Father’s age =
zy
zyt 1
I am three times as old as my son. Five years later, I shall be two
and half times as old as my son. How old am I and how old is my
son?
Son’s age =
2
1
23
51
2
1
2
= 15 years. Father’s age = 15 x 3 = 45 years.

4. • 9. A person’s present age is two–fifth of the
age of his mother. After 8 years, he will be
one–half of the age of his mother. How old is
the mother at present?
Mother’s age =
zy
tz 1

5. • A man is 24 years older than his son. In two years,
his age will be twice the age of his son. The
present age of his son is
• Let Son’s age = x.
• Then Father’s age is 24 + x
• After two years
• 2(x +2) = 24+ x +2
• 2x + 4 = 26 + x
• X = 22.

6. Formula 3
• T1 years earlier the age of father was x times the age of his son.
• T2 years hence, the age of the father becomes z times the age of his
son.
• What are the present age of the son and the father?
Son’s age =
zx
xtzt 11 12
Two years ago, a man was six times as old as his son. After 18
years, he will be twice as old as his son. What is their present
ages(in years) ?
Son’s age =
26
1621218
and Father’s age = 32.

7. • 11. The age of father 10 years ago was thrice
the age of his son. Ten years hence, father’s
age will be twice that of his son. The ratio of
their present ages is:
Son’s age =
zx
xtzt 11 12
Here t1 = 10 and t2 = 10 . Z = 2 and X =
3Hence Son’s age = 30.
Father’s age 10 years ago was 60.
Present age = 70. The ratio is 7: 3

8. Formula 4
• The ratio of the ages of the father and the son at
present is x:y. t years earlier, the ratio was a:b. What
are the present ages of the son and the father?
Son’s age=
productcrossofdifference
bat
y
Father’s age =
productcrossofdifference
bat
x
The present age of a man is double the age of his son. After 8
years, the ratio of their ages will be 7:4. Find the present ages of
the man and his son
Present age = 2:1 and After 8 years = 7:4.
Son’s age =
1742
478
1 = 24 years. Man’s age =
1742
478
2
= 48 years.

9. Formula 5
• The sum of the ages of a father and his son is x. After y years,
the age of the father will be t times that of his son. What is
the age of his son?
Son’s age = 1Times
1)-(TimesagoyearsofNoagesofSum
The sum of the ages of a father and his son is 45 years. 5 years
ago, the age of the father will be four times that of his son. What
is the age of his son?
Son’s age =
14
14545
= 12 years.

10. • 4. The sum of the present ages of a father and
his son is 60 years. Six years ago, father’s age
was five times the age of the son. After 6
years, son’s age will be
Son’s age = 1Times
1)-(TimesagoyearsofNoagesofSum
Son’s age =
15
15660
= 14 years.
After six years son’s age will be 20 years.

11. • Q is as much younger than R as he is older
than T. If the sum of the ages of R and T is 50
years, what is definitely the difference
between R and Q’s age?
• Cannot be determined.
• Clearly Q is the arithmetic mean of R and T.
Hence age of Q will be 25. Still we could not
determine the value of R.

12. Purchasing a chicken