Age Problems : Tricks
AGE
The age difference between two persons remains constant throughout their life. If two persons are born at different times, their age difference never changes.
Formulas:
1. After “t” years:
o Present age of P = x, Q = y → After t years:
P = x + t, Q = y + t
2. “t” years ago:
o Present age of P = x, Q = y → t years ago:
P = x − t, Q = y − t
3. Age difference:
o Difference = x − y (remains constant)
Tip for Exams:
- Always check the age difference first.
- Use the difference to quickly solve “after t years” or “t years ago” problems.
- This trick saves time in competitive exams like SSC, Bank, Railways, and other job exams.
Q. The sum of mother's and son's ages is 70. If mother is 40 years older than son, what is son's age ?
(a) 8 years (b) 10 years (c) 12 years (d) 15 years
Soln.
Let son’s age = x
Mother’s age = x + 40
According to question: x + (x + 40) = 70
Simplify: 2x + 40 = 70
Subtract 40 from both sides: 2x = 30
Divide by 2: x = 15
Son’s age = 15 years
Q. A brother is 12 years old and his sister is 4 years younger. What is the sister's age ?
(a) 6 years (b) 7 years (c) 8 years (d) 9 years
Soln.
Brother’s age = 12 years
Sister is 4 years younger → 12 − 4 = 8 years
Q. The sum of mother's and son's ages is 50. If mother is 30 years older than son, what is son's age ?
(a) 8 years (5) 10 years (c) 12 years (d) 15 years
Soln.
Let the son’s age = x
Then, mother’s age = x + 30
According to the question:
x + (x + 30) = 50
⇒ 2x + 30 = 50
⇒ 2x = 20
⇒ x = 10 years
Q. A man is 60 years old at present. What will be his age after 12 years ?
(a) 72 years (b) 65 years (c) 68 years (d) 80 years
Soln.
Present age of the man = 60 years
After 12 years, his age will be:
60 + 12 = 72 years
Q. The father's age is three times the son's age. If father's age is 45 years, what is the son's age?
(a) 12 years (b) 15 years (c) 18 years (d) 20 years
Soln.
Father’s age = 3 × Son’s age
⇒ 45 = 3 × Son’s age
⇒ Son’s age = 45 ÷ 3 = 15 years
Q: The average age of 10 persons increases by 2 years when one of them, aged 25 years, is replaced by a new person. What is the age of the new person ?
Soln:
Increase in total age = Number of persons × Increase in average
= 10×2 = 20 years
So,
New person’s age = Old person’s age + Increase in total age
= 25 + 20 = 45
Ans: 45 years
Q. A man is 30 years old at present. What will be his age after 5 years ?
(a) 35 years (b) 36 years (c) 38 years (d) 40 years
Given:
Present age = 30 years
After 5 years → add 5
30 + 5 = 35
Ans: (a) 35 years
Q. A brother is 25 years old and his sister is 12 years younger. What is the sister's age ?
a (a)13 years (b) 17 years (c) 18 years (d) 19 years
Given:
Brother’s age = 25 years
Sister is 12 years younger ⇒ subtract 12
25−12=1325 - 12 = 1325−12 = 13
Ans: (a) 13 years
Q. The father's age is five times the son's age. If father's age is 90 years, what is the son's age ?
(a) 12 years (b) 15 years (c)-18 years (d) 20 years
Given:
Father’s age = 90 years
Father’s age = 5 × Son’s age
So,
Son’s age = 90 / 5 = 18
Ans: (c) 18 years
Q. Ram is 5 years older than Shyam. If Ram is 20 years old, what is Shyam's age?
(a) 10 years (b) 12 years © 15 years (d) 18 years
Given:
Ram is 5 years older than Shyam.
Ram’s age = 20 years
So,
Shyam’s age = 20 – 5 = 15
Ans: (c) 15 years
Q. The sum of mother's and son's ages is 70. If mother is 40 years older than son, what is son's age ?
(a) 8 years (b) 10 years (c) 12 years (d) 15 years
Given:
Let the son’s age = x
Then mother’s age = x + 40
According to the question,
X + (x + 40) = 70
2x + 40 = 70
2x + 40 = 70
2x = 30
x=15
Son’s age = 15 years
Ans: (d) 15 years
Q. A brother is 12 years old and his sister is 4 years younger. What is the sister's age ?
(a) 6 years (b) years (c) 8 years (d) 9 years
Soln:
Brother’s age = 12 years
Sister is 4 years younger ⇒ 12 – 4 = 8
Ans: (c) 8 years
Q. A man is 30 years old at present. What will be his age after 5 years ?
(a) 35 years
(b) 36 years
(c) 38 years
(d) 40 years
Soln.
The man’s current age = 30 years
After 5 years, his age will be: 30 + 5 = 35 years
Ans: (a) 35 years
Q. A brother is 25 years old and his sister is 12 years younger. What is the sister's age ?
(a) 13 years
(b) 17 years
(c) 18 years
(d) 19 years
Soln.
Brother’s age = 25 years
Sister is 12 years younger → 25 − 12 = 13 years
Ans: (a) 13 years