A father is 40 and his son is 10. After how many years will the father be 3 times as old as the son?
40 + x = 3(10 + x)
40 + x = 30 + 3x → 2x = 10
x = 5
Answer: 5 years
Problems on Ages · Exercise 4 of 6
65 mixed-level problems on ages in the style of campus placement tests, SSC CGL/CHSL/MTS, RRB NTPC and Group D, IBPS/SBI, UPSC CSAT and state exams. Use them as a timed revision set.
A father is 40 and his son is 10. After how many years will the father be 3 times as old as the son?
40 + x = 3(10 + x)
40 + x = 30 + 3x → 2x = 10
x = 5
Answer: 5 years
A is one-third as old as B, who is 36. How old will A be after 4 years?
A now = 36 ÷ 3 = 12
After 4 years = 16
Answer: 16 years
Two people's ages are in the ratio 2 : 5 and add up to 49. How old is the elder?
7k = 49 → k = 7
Elder = 5 × 7 = 35
Answer: 35 years
Six years from now the ages of A and B will be in the ratio 5 : 4. Their present ages add up to 33. How old is A?
4(a + 6) = 5(b + 6) and a + b = 33
4a + 24 = 5(33 − a) + 30
9a = 171 → a = 19
Answer: 19 years
A and B are 60 years old together, and A is 6 years more than twice B. How old is A?
a = 2b + 6
3b + 6 = 60 → b = 18
a = 42
Answer: 42 years
A son was born when his father was 24. The ratio of their present ages is 3 : 5. How old is the son?
f = s + 24 and 5s = 3f
5s = 3s + 72 → s = 36
Answer: 36 years
A man born in 1985 married at the age of 28. In which year did he marry?
Year of marriage = 1985 + 28
= 2013
Answer: 2013
The ages of a grandfather and his grandson are in the ratio 9 : 1, and the grandfather is 64 years older. How old is the grandson?
9k − k = 64 → 8k = 64
k = 8
Answer: 8 years
Ten years ago the ratio of the ages of X and Y was 1 : 2. Ten years from now it will be 3 : 4. How old is Y now?
y − 10 = 2(x − 10) → y = 2x − 10
4(x + 10) = 3(y + 10) = 3(2x)
4x + 40 = 6x → x = 20
y = 30
Answer: 30 years
The total age of A and B is 12 years more than the total age of B and C. How many years younger is C than A?
(A + B) − (B + C) = 12
B cancels: A − C = 12
C is 12 years younger than A
Answer: 12 years
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