Problems on Ages – Tips and Tricks with solved examples

Problems on ages are easy to attempt. Just pay attention to the concepts and solve some numericals on it. Though we have tried to showcase all type of problems on ages, if you find any type missing in this post do submit the problems through the form provided at the end of this post.

Formulas and Quick Tricks for Problems on Ages

1. If the current age is x, then age n years later/hence = x + n
2. If the current age is x, then age n years ago = x – n
3. The ages are in a ratio a : b will be ax and bx.
4. If the current age is x, then n times the age = nx
5. If the current age is x, then 1/n of the age is x/n

Questions and Solved Examples for Problems on Ages

Question: Present age of Rahul is 5 years less that Ritu’s present6 age. If 3 years ago Ritu’s age was x, which of the following represents Rahul’s present age?
(a) (x+3)
(b) (x-2)
(c) (x-3+8)
(d) (x+3+8)

Ans: (b) x-2

Explanation:

3 years ago, Ritu’s age was = x years

So, Ritu’s present age is = (x+3) yr

Hence Rahul’s present age = (x+3-5) yr = (x-2) yr

Question: The difference between present ages of Arun and Deepak is 14 years. 7 years ago, the ratio of their ages was 5:7 respectively. What is Deepak’s present age?
(a) 49 years
(b) 42 years
(c) 63 years
(d) None of these

Ans: (d) None of these

Explanation:

Let’s say, 7 years ago age of Arun and Deepak was 5x and 7x respectively

So, Arun’s present age = (5x+7) years

And Deepak’s present age = (7x+7) years

Difference in their age is = 2x

So, 2x = 14

⇒ x =7

So, Deepak’s present age = (7x+7) = (7×7+7) = 56 years

Question: Father’s age is 30 years more than son’s age. Then years hence the father’s age will become three times the son’s age that time. What is son’s present age in years?
(a) 8
(b) 7
(c) 5
(d) Cannot be determined

Ans: (c) 5

Explanation:

Say, son’s present age = x years

So, father’s present age = (x+30) years

After 10 years son’s age = (x+10) years

And fathers age = (x+30+10) = (x+40) years

According to condition,

x+40 = 3(x+10)

⇒ x+40 = 3x+30

⇒ 2x = 10

⇒ x = 5

Question: If twelve years hence a man is going to be 1\displaystyle\frac{1}{3} his age twelve years ago, what is his present age?
(a) 24 years
(b) 72 years
(c) 96 years
(d) 84 years

Ans: (d) 84 years

Explanation:

Say, present age = x years

Age 12 years ago = (x-12) years

Age after 12 years = (x+12) years

So, x+12 =  1\displaystyle\frac{1}{3} (x-12)

⇒ x+12 =  \displaystyle \frac{4}{3} (x-12)

⇒ 3x+36 = 4x -48

⇒ x =84

Question: A is much younger to B as he is elder to C. If the sum of ages of B and C is 48 years, what is the age of A in years?
(a) 20
(b) 24
(c) 30
(d) 32

Ans: (b) 24

Explanation:

As per condition,

B-A = A-C

⇒ 2A = B+C

⇒ 2A = 48

⇒ A = 24

Question: The ages of Melwyn and Louis are in the ratio of 7:10. After 6 years the ratio of their ages will be 17:23. What is the difference in their ages?
(a) 8 years
(b) 4 years
(c) 12 years
(d) 10 years

Ans: (b) 12 years

Explanation:

Say, present age of Melwyn = 7x years

And present age of louis = 10x years

As per condition, \displaystyle \frac{7x+6}{10x+6}=\frac{17}{23}

                        ⇒ 170x + 102 = 161x + 138

                        ⇒ 9x = 36

                        ⇒ x = 4

Difference in ages = 10x – 7x = 3x = 3×4 = 12

Question: Karan is 60 years old and Arjun is 80 years old. How many years their age ratio was 2:3?
(a) 10 years
(b) 15 years
(c) 20 years
(d) 25 years

Ans: (c) 20 years

Explanation:

Let’s say x years ago the ratio was 2:3

So,     \displaystyle \frac{60-x}{80-x}=\frac{2}{3}

⇒ 160 – 2x = 180 -3x

⇒ x = 20

Question: The age of Mr. Bhagat in 2002 was \displaystyle \frac{1}{90} of his birth year. What was his age on 2006?
(a) 30
(b) 28
(c) 26
(d) 22

Ans: (c) 26

Explanation:

Say, Mr. Bhagat’s birth year is = x

As per condition, 2002-x=\displaystyle \frac{x}{90}

                        ⇒ 180180 – 90x = x

                        ⇒ 91x = 180180

                        ⇒ x = 1980

So, his age at 2006 = 2006 – 1980 = 26