Amit’s father is aged five times more than Amit. After 6 years, he would be three and a half times of Amit’s age. After further 9 years, how many times of Amit’s age would he be?
- (a)
- (b)
- (c)
- (d)
Answer
Why
Correct — B. Read 'five times more than' as six times as old — Amit's own age plus five times it. That is the reading the option list supports.
Let Amit be x, so his father is 6x.
After 6 years: 6x + 6 = 3.5(x + 6)
6x + 6 = 3.5x + 21
6x − 3.5x = 21 − 6
2.5x = 15
x = 6
Today Amit is 6 and his father is 36. Check: after 6 years, 42 = 3.5 × 12.
'After a further 9 years' means 15 years from today: Amit 21, father 51.
51 ÷ 21 = 17⁄7
= 2 3⁄7 times → option (b), the image reading 2 3⁄7 times.
Why the others are wrong
- (a)2 1⁄4 would put the father at 47¼ years when Amit is 21 — not a whole number of years, and impossible once Amit's present age comes out as 6.
- (c)2 3⁄4 needs a father of 57¾ against Amit's 21. The gap between them is fixed at 30 years, so at 21 the ratio can only be 51⁄21.
- (d)3 2⁄7 keeps the right denominator but overshoots. 23⁄7 would need the father at 69 when Amit is 21, a gap of 48 years rather than the fixed 30.
Concept
Age problems are two linear equations in disguise, and the fastest guard on any answer is that the difference of two ages never changes. Here it is 36 − 6 = 30 years, at every date in the question.
Set the present ages from the first sentence, apply the second condition at its own date, and solve. The third date then needs no new algebra — just add the years to both ages.
Count the dates carefully. 'After a further 9 years' is measured from the 6-year mark, so the final ratio is taken 15 years from today, not 9.
The stem's wording is 'five times more than'. Taken as plain 5 × Amit's age, it gives Amit = 10 and a father of 50.
That route ends at 65⁄25 = 2 3⁄5, which none of the four options carries.
The reading that lands on an option is age + 5 × age = 6 ×, and the key follows it.
Key facts
- The difference between two ages is constant, here 30 years.
- Amit is 6 today and his father 36, which satisfies 42 = 3.5 × 12 after six years.
- 'After a further 9 years' counts from the 6-year mark, so it is 15 years from the present.
- 51⁄21 reduces to 17⁄7, which is 2 3⁄7.
Study next
Common traps
- Taking 'after further 9 years' as 9 years from today rather than 15.
- Reading 'five times more than' as exactly five times, which gives 2 3⁄5 and no matching option.
- Inverting the final ratio and reporting Amit's age as a fraction of his father's.
Two-condition age problems recur with the wording rearranged — 9 Sep 2024, 12:30, Quant Q.6 (four times seven years ago, two-and-a-half times four years from now) and 24 Sep 2024, 16:00, Quant Q.6 (twice one year ago, 4 : 3 after nine years).
Related PYQs
No directly related past PYQ was found.