# GMAT word problems - Problems on Ages

**Aptitude Questions with Answers – Problems on Ages 11**

11. The ratio of the present age of A and B is 1:2 and 5 years ago, the ratio of their ages was 1:3. What will be the ratio of their ages after 5 years?

a)2:3 b)4:7 c)3:5 d)7:8

**Answer :C**

**Explanation:**Let the present ages of A and B be x and 2x years respectively.

5 years ago, their ages were x-5 and 2x-5.

5 years ago, their ages were in the ratio of 1:3.

A’s age 5 years ago/ B’s age 5 years ago =

1
3

=>

x-5
2x-5

=
1
3

=>3x-15=2x-5 =>x=10.
Their present ages are 10 and 20.

After 5 years, their ages will be 10+5 and 20+5 = 15 and 25

Ratio of their ages after 5 years =15:25 = 3:5

**Quantitative Aptitude for CAT – Age related problems**

12.The sum of the ages of 5 girls each both at 3 years intervals is 60 years. What is the age of eldest girl?

a)12 years b)16 years c)18 years d)20 years

**Answer: C**

**Explanation :**Let the age of the youngest girl be x.

Then each both at 3 years interval, the ages will be x ,x+3, x+6, x+9 ,x+12 .

=>5x+30=60 >x=6.

Therefore, age of the eldest girl= x+12 =6+12=18.

**Aptitude Problems with Answers – Problems on Ages**

13. A’s grandfather was 8 times older to him 16 years ago. His grandfather would be 3 times of his age 8 years from now. 8 years ago, what was the ratio of A ‘s age to that of his grandfather’s age?

a)53:11 b)12:47 c)11:53 d)19:21

**Answer: C**

**Explanation :**Let 16 years ago, A’s age be x and his grandfathers be 8x.

Present age of A is x+16 and and grandfathers is 8x+16

After 8 years, A’s age will be x+24 and his grandfather’s age will be 8x+24.

After 8 years, grandfather will be 3 times of A.

Grandfather’s age after 8 years
A’s age after 8 years

=
3
1

8x+24
x+24

=
3
1

=>8x+24=3x+72=> x=

48
5

Ratio of their ages 8 years ago

=>x+8: 8x+8 =

=>x+8: 8x+8 =

48
5

+8 : 8 x
48
5

+ 8 = 11:53**GMAT Word Problems – Problems on Ages**

14. At present age of the mother is 5 times that of the age of her daughter. After 3 years, age of the mother would be 4 times the age of her daughter. What is the age of the daughter after 3 years?

a)12 years b)15 years c)17 years d)20 years

**Answer : A**

**Explanation :**Mother’s age is 5 times the age of the daughter.

Let age of the daughter be x and age of the mother be 5x.

After 3 years, their ages will be x+3 and 5x+3.

Given that after 3 years, age of mother will be 4 times the age of daughter.

The ratio of the ages of mother and daughter after 3 years = 4:1

Therefore,

5x+3
x+3

=
4
1

=>5x+3 = 4x+12
=>x=9

Present age of the daughter is 9 years.

After 3 years, age of the daughter will be x+3 = 9+3 = 12 years

**Aptitude Questions with Explanations – Problems on Ages**

15. A teacher is 3 times as old as his student. 5 years hence, teacher will be 2 ½ times as old as his student. What is the difference between the ages of teacher and student?

a)40 years b)50 years c)60 years d)5 years

Answer :

Explanation: Let the age of the student be x years . Teacher’s age = 3x

After 5 years, their ages will be x+5 and 3x+ 5.

After 5 years, their ages will be in ration: 1: 2 ½ =2:5

x+5
3x+5

=
2
5

=>5 (x+5)= 2(3x+5) =>5x+25=x+10 =>x=15 years.
The difference between their ages is=>3x-x=2x =2 x 15 = 30 years

**Problems on Ages solved problems for Competitive Exams**

16. 6 years ago, the ratio of ages of A and B was 5:6 and 4 years hence, the ratio of their ages will be 10:11. What is the present age of B?

a) 10 years b) 12 years c)15 years d)16 years

Answer:

Explanation:

6 years ago, the ages of A and B were in the ratio of 5:6.

6 years ago, let the age of A and B were 5x and 6x .

Their present ages = 5x+6 and 6x+6

After 4 years , their ages will be in the ratio 10:11

After 4 years , age of A and B will be 5x+6+4 and 6x+ 6 +4 => 5x+10 and 6x+10

5x+10
6x+10

=
10
11

=>55x+110 = 60x+100 => x=2.
Present age of B= 5x+6 = 5 x 2 +6 =16 years

**Aptitude for Campus Placements : Problems on Ages solved questions 17.**

17. The sum of the ages of a father and son is 50 years. 5 years ago, the age of the father was 7 times the age of the son. What will be age of the father after 7 years?

a)42 years b)35 years c)45 years d)49 years

**Answer: D**

**Explanation:**5 years ago, the age of the father was 7 times the age of the son.

5 years ago , the age of the son was x and father was 7x.

Present sum of the ages of father and son = 50 years

5 years ago, their sum of the ages was 50 – 2x5 = 40 years

Age of the father , 5 years ago= 40 x

7
8

=35 years
Present age of the father= 35+5 = 40 years

After 9 years, age of the father will be = 40 +7 = 47 years.

**GMAT Quantitative Aptitude study material – Problems on Ages**

18. The ratio of the ages of A and B is 1:4 and the product of their ages is 256. What will be the ratio of their ages after 8 years?

a) 3:5 b)10:3 c)3:10 d)None of these

**Answer :C**

**Explanation**: let the age of A and B be x and 4x.

Product of their ages = x x 4x =4x

^{2}=256 =>x=8
Present age of A and B = x and 4x = 8 years and 32 years

Ratio of their ages after 8 years will be = 8+8 : 32+8

=16:40= 2:5

**Arithmetic free study material- Age related Problems**

19. At the time of marriage Siva was 6 years elder to his wife and 12 years after the marriage his age was

6
5

times the age of his wife. What was the age of his wife at the time of marriage?
a) 20 years b)24 years c)28 years d)32 years

**Answer : B**

**Explanation :**Let the age of Siva at the time of marriage be x years.

Then, age of Siva’s wife at the time of marriage = x-6 years

After 12 years , ratio of their ages was 6:5.

The difference between their ages = 6-5= 1 part = 6 years

Their ages 12 years after their marriage were 6x6 and 5x6 = 36 and 30.

At the time of marriage, their ages were, 36-12 and 30-12 = 24 and 18

Therefore, at the time of marriage, age of Siva's wife was =18 years

**Aptitude Questions with Explanations – Problems on Ages**

20. After 15 years the age of Murthy will be 4 times the age
which was 15 years ago. Find the present age of Murthy?

a) 25 years b)30
years c)35 years d)40 years

**Answer: A**

**Explanation:**Let the present age of Murthy be x years.

15 years ago, his age was= x-15.

After 15 years, his age will be = x+15

After
15 years , he will be 5 times the age which was 20 years ago

=>(x+15) =4(x-15)

=> 4x-60= x+15 =>x= 25 years

Alternate
method:

The ratio of the ages of Murthy 15
years ago and 15 years hence= 4:1

The difference between these two = 15
+15 = 30 years

4-1 = 3 parts = 30 years =>1
part=10

Age of Murthy after 15 years = 4x 10 = 40
years

Therefore, present age of Murthy =
40-15 = 25 years.