To
solve problems on ages, student should have knowledge of ratios and linear equations.
Here problems usually involve comparison of ages in the present, several years
ago or several years from now.

**Linear Equation:**

An
equation involving only one unknown variable is a linear equation.

**Problems on Ages.**

**Aptitude Questions with Answers – Problem on Ages 1**

The present ages of A,B and C are in the ratio of 5:7:8. Seven
years ago, the sum of their ages was 59.What is the present age of eldest one?

a)20 years b)28 years c)32 years d)40 years

**Answer :C**

**Explanation:**Let their present ages be 5x, 7x and 8x.

7 years ago, sum of their ages was 59.

Sum
of their present ages = 59 +( 3 x 7) = 80

Sum
of their present ages given is 5x + 7x + 8x = 20x

20x = 80 =>x =

80
20

=4
Age
of the Eldest one= 8x = 8x 4 = 32 years.

**Word Problems for GMAT – Age related problems 2**

In Ravindra Bharathi School, there are 80 boys of age 14 each,
70 boys of age 15 each and 50 boys of age 13 each and another 60 boys of age 12
each. The average age of the boys of the school is

a)
13.6 years b)12.5 years c)13 years d)14.2 years

**Answer: A**

**Explanation:**

Average
age of boys = Sum of the ages of all boys/ Total number of boys

=

(80 x14)+(70x15)+(50x13)+(60x12)
(80+70+50+60)

=

(1120+1050+650+720)
260

=3540/260 =13.6

**Aptitude questions with explanations : Problems on Ages 3**

Three years ago, the average age of P and Q was 20 years. With R
joining them, their average age becomes 23 years. What is the age of R?

a)18 years b)20
years c)23 years d)25 years

Answer
:C

Explanation: Three years ago, the average age of P and Q
was 20 years.

Three years ago, their sum of the
ages was 2x20= 40 years

Present age of P+Q+R = 3 X23 =69

Present age of P+Q=40+( 2 x 3)= 46

Present
age of R = ( P+Q+R)- (P+Q)= 69-46 =23
years

**Arithmetic study material – Age related problems 4**

The average age of 4 boys
is 14 years. Their ages are in the ratio of 3:5:4:2. Find the age of the
youngest boy ?

a) 8 years b)6
years c)12 years d)14 years

**Answer :A**

**Explanation :**

Sum of the ages of 4 boys = Average x Number of Boys = 4x 14 = 56

Age of the youngest boy =
56 x

2
14

= 8 years**Quantitative aptitude for CAT – Problems on Ages 5**

The ratio between the ages of Shastri and Varma is 5:6 and sum
of their ages is 55 years. What is the ratio of their ages after 5 years ?

a) 3:4 b)4:5 c)5:6 d)6:7

**Answer:D**

**Explanation:**Present age of Shastri= 55 x

5
11

= 25 years
Present age of Varma = 55 x

6
11

= 30 years
After
5 years, age of shastri will be = 25 +5
= 30 years , Age of Varma will be =
30+5 =35 years

Ratio
of their ages after 5 years will be = 30: 35 = 6 :7

**Aptitude questions and word problems – Ages 6**

6.
The ratio between the present age of Sudheer and
Sravani is 7:8. If Sravani is 5 years older than Sudheer, what will be the
ratio of their ages after 10 years ?

a) 8:9 b)9:10 c)5:7 d)6:4

Answer:

Explanation
: Let present age of Sudheer and Sravani be 7x and 8x years respectively.

Sravani
is 5 years older than Sudheer, means the difference between their ages is 5
years

Difference of ages = 8x- 7x = x = 5 years

Present
age of Sudheer and Sravani => 7 x5 =35 years and 8x5 = 40 years

After
10 years , their ages will be = 35+
10 and 40+10

Ratio
of the ages of Sudheer and Sravani after 10 years = 45 : 50 = 9:10

**Quantitative Aptitude Questions and Answers – Problems on Ages**

7. The sum of the present ages of a father and his son is 60
years. Six years ago, the father’s age was 5 times the age of the son. What
will be the age of son after 7 years?

a)21 years b)19
years c)15 years d)13 years

**Answer: A**

**Explanation:**

Let
the fathers and sons present age be x and y.

Given
sum of the ages of father and son is 60 years =x+y=60

Six
years ago, fathers age was 5 times the age of the son => F =5 x S

Ratio
of their ages was = 5:1

Six
years ago. Sum of the their ages = 60 – (2 x6) =48

Age
of the son , 6 years ago = 48 x

1
6

= 8 years
Present
age of son = 8 years + 6 = 14 years

Age
of the son after 7 years = 14 +7 = 21 years

**Aptitude Problems on Ages – GMAT Word Problems**

8. The age of Sharma and Tripathi differ by 18 years. 6 years
ago, Sharma was 3 times as old as Tripathi. What is the present age of Sharma?

a)28 years b)30
years c)32 years d)33 years

**Answer :D**

**Explanation :**The difference between the ages of Sharma and Tripathi is 18 years.

The
age difference is always same.

6
years ago, ratio of the ages of Sharma and Tripathi => Sharma= 3 Tripathi
=> 3:1

Their age difference is 3x-x = 2x = 18 years
=>x = 9 years

6
years ago , age of Sharma = 3x = 3 x 9
= 27 years.

Present age of Sharma= 27+ 6 = 33 years.

**Aptitude Questions with Explanations : GRE Word Problems**

9.
One year ago, the ratio of ages of A and B was 6:7. After 4 years, their ratio
of the ages will be 7:8. What is present age of B ?

a)30
years b)36 years c)40 years d)42 years

**Answer :B**

**Explanation:**One year ago, their ages were be 6x and 7x.

Present
ages of A and B are 6x+1 and 7x+1

After 4 years, age of A will be 6x+1+4 and age of B will be 7x+1+4 =>6x+5 and
7x+5.

After
4 years, their ages will be in the ratio 7:8.

A
age after 4 years/B’s age after 4 years =

7
8

=>

6x+5
7x+5

=
7
8

=>48x+
40=49x+35 =>x=5

Present
age of B = 7x+1 = 7x5+1 =36.

**Aptitude Questions with Solutions : Problems on Ages 10**

10. Present ages of A and B are in the ratio 6:7 respectively. 8
years hence, the ratio of the ages will be 8:9 respectively. What is the
present age of A ?

a)24 years b)28
years c)36 years d)40 years

Answer
: A

Explanation: Let the present ages of A and B be 6x and 7x
years.

After
8 years, their ages will be 6x+8 and 7x+8.

After
8 years, their ages will be in the ratio 8:9.

A
‘s age after 8 years/B’s age after 8 years =8/9

=>

6x+8
7x+8

=
8
9

=>54x+
72=56x+64 =>2x=8=>x=4

Present
age of A = 6x= 6 x 4 =24 years.