Mathematics Questions for Competitive Exam

Problem on Age 1. Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
A. 45	B. 40
C. 35	D. 30

2. Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil's age. After further 8 years, how many times would he be of Sunil's age?
A. 4 times	B. 4 times
C. 2 times	D. 3 times

3. A man's age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10 years. What is his present age?
A. 70	B. 60
C. 50	D. 40

4. A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
A. 23 years	B. 22 years
C. 21 years	D. 20 years

5. Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Syam's present age in years?
A. 28	B. 27
C. 26	D. 24

6. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. Find out the age of the youngest child?
A. 6 years	B. 5 years
C. 4 years	D. 3 years

7. A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27. How old is B?
A. 10	B. 9
C. 8	D. 7

8. The Average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
A. 48	B. 45
C. 43	D. 44

9. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, what was the son's age five years back?
A. 20 years	B. 18 years
C. 14 years	D. 22 years

10. Ayisha's age is 1/6th of her father's age. Ayisha 's father's age will be twice the age of Shankar's age after 10 years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha 's present age.
A. 10 years	B. 12 years
C. 8 years	D. 5 years

Answer With Explanation

1. Answer : Option C

Explanation :

Let the present age of P and Q be 3x and 4x respectively.

Ten years ago, P was half of Q in age

=> (3x – 10) = ½ (4x – 10)

=> 6x – 20 = 4x – 10

=> 2x = 10

=> x = 5

total of their present ages = 3x + 4x = 7x = 7 × 5 = 35

2. Answer : Option C

Explanation :

Assume that Sunil's present age = x.

Then father's present age = 3x + x = 4x

After 8 years, fathers age = 2 ½ times of Sunils' age

=> (4x+8) = 2 ½ × (x+8)

=> 4x + 8 = (5/2) ×(x + 8)

=> 8x + 16 = 5x+ 40

=> 3x = 40-16 = 24

=> x = 24/3 = 8

After further 8 years,

Sunil's age = x + 8+ 8 = 8+8+8 = 24

Father's age = 4x + 8 + 8 = 4 × 8 + 8 + 8 = 48

Father's age/Sunil's age = 48/24 = 2

3.Answer : Option C

Explanation :

Let the age before 10 years = x

Then 125x/100 = x + 10

=>125x = 100x + 1000

=> x = 1000/25 = 40

Present age = x + 10 = 40 +10 = 50

4.Answer : Option B

Explanation :

Let the present age of the son = x years

Then present age the man = (x+24) years
Given that in 2 years, man's age will be twice the age of his son

=> (x+24) +2 = 2(x+2)

=> x = 22

5. Answer : Option D

Explanation :

Ratio of the present age of Kiran and Syam = 5 : 4

=> Let the present age of Kiran = 5x

Present age of Syam = 4x
After 3 years, ratio of their ages = 11:9

=> (5x + 3) : (4x + 3) = 11 : 9

=> (5x+3) / (4x+3) = 11/9

=> 9(5x + 3) = 11(4x + 3)

=> 45x + 27 = 44x + 33

=> x = 33-27 =6

Syam's present age = 4x = 4×6 = 24

6.Answer : Option C

Explanation :

Let the age of the youngest child = x

Then the ages of 5 children can be written as x, (x+3), (x+6),(x+9) and (x+12)

X + (x+3) + (x+6) + (x+9) + (x+12) = 50

=> 5x + 30 =50

=> 5x = 20

=> x = 20/5 = 4

7.Answer : Option A

Explanation :

Let the age of C = x. Then

Age of B = 2x

Age of A = 2 + 2x

The total age of A,B and C =27

=> (2+2x) + 2x + x = 27

=> 5x = 25

=> 25/5 = 5
B's age = 2x = 2×5 = 10

8. Answer : Option D

Explanation :

Total age of all students = 22×21

Total age of all students + age of the teacher = 23 × 22

Age of the teacher = 23×22 – 22×21 = 22(23-21) = 22×2 = 44

9. Answer : Option C

Explanation :

Let the son's present age be x years.

Then, (38 - x) = x

=> 2x = 38

=> x = 38/2 = 19

Son's age 5 years back = 19-5 = 14

10.Answer : Option D

Explanation :

Consider Ayisha's present age = x

Then her father's age = 6x

Given that Ayisha 's father's age will be twice the age of Shankar's age after 10years

=> Shankar's age after 10 years = ½(6x + 10) = 3x + 5

Also given that Shankar's eight birthdays was celebrated two years before =>

Shankar's age after 10 years = 8 + 12 = 20

=> 3x + 5 = 20

=> x = 15/3 = 5

=> Ayisha 's present age = 5 years