# PROBLEMS ON AGES

1. Father is aged three times more than his son Ali’s. After 8 years, he would be two and a half
times of Ali’s age. After further 8 years, how many times would he be of Ali’s age?

A. 2 times
B. 2 1/2 times
C. 2 3/4 times
D. 3 times
Answer: Option A
Explanation:
Let Ali’s present age be x years. Then, father’s present age =(x + 3x) years = 4x years.
(4x + 8) = 5/2 (x + 8)
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio =(4x + 16)/(x + 16)=48/24=2

2. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
A. 4 years
B. 8 years
C. 10 years
D. None of these
Answer: Option A
Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.

3. 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, the son’s age five years back was:
A. 14 years
B. 19 years
C. 33 years
D. 38 years
Answer: Option A
Explanation:
Let the son’s present age be x years. Then, (38 – x) = x
2x = 38.
x = 19.
Son’s age 5 years back (19 – 5) = 14 years.

4. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C
be 27, the how old is B?

A. 7
B. 8
C. 9
D. 10
E. 11
Answer: Option D
Explanation:
Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B’s age = 2x = 10 years.

5. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years?
A. 24
B. 27
C. 40
D. Cannot be determined
E. None of these
Answer: Option A
Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, 5x + 3=11
4x + 3= 9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x – 44x = 33 – 27
x = 6.
Anand’s present age = 4x = 24 years.

6. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A. 14 years
B. 18 years
C. 20 years
D. 22 years
Answer: Option D
Explanation:
Let the son’s present age be x years. Then, man’s present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.

7. Six years ago, the ratio of the ages of Usman and Rauf was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Rauf’s age at present?
A. 16 years
B. 18 years
C. 20 years
D. Cannot be determined
E. None of these
Answer: Option A
Explanation:
Let the ages of Usman and Rauf 6 years ago be 6x and 5x years respectively.
Then, (6x + 6) + 4=11
(5x + 6) + 4= 10
10(6x + 10) = 11(5x + 10)
5x = 10
x = 2.
Rauf, present age = (5x + 6) = 16 years.

8. The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be:
A. 12 years
B. 14 years
C. 18 years
D. 20 years
Answer: Option D
Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 – x) – 6 = 5(x – 6)
54 – x = 5x – 30
6x = 84
x = 14.
Son’s age after 6 years = (x+ 6) = 20 years..

9. At present, the ratio between the ages of Fazal and Bilal is 4 : 3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present ?
A. 12 years
B. 15 years
C. 19 and half
D. 21 years
Answer: Option B
Explanation:
Let the present ages of Fazal and Bilal be 4x years and 3x years respectively. Then,
4x + 6 = 26 4x = 20
x = 5.
Bilal’s age = 3x = 15 years.

10. Sohail is younger than Rizwan by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
A. 16 years
B. 18 years
C. 28 years
D. 24.5 years
E. None of these
Answer: Option D
Explanation:
Let Rizwan’s age be x years.
Then, Sohail’s age = (x – 7) years. x – 7/x=7/9
9x – 63 = 7x
2x = 63
x = 31.5
Hence, Sohail’s age =(x – 7) = 24.5 years.

11. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
A. 8, 20, 28
B. 16, 28, 36
C. 20, 35, 45
D. None of these
Answer: Option B
Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x – 8) + (7x – 8) + (9x – 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

12. Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the
ages of her parents?

A. 2 years
B. 4 years
C. 6 years
D. 8 years
Answer: Option C
Explanation:
Mother’s age when Ayesha’s brother was born = 36 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 36) years = 6 years.

13. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
A. 32 years
B. 36 years
C. 40 years
D. 48 years
Answer: Option C
Explanation:
Let the mother’s present age be x years.
Then, the person’s present age = (2/5)x years.
(5/2x+8)=1/2 (x + 8)
2(2x + 40) = 5(x + 8)
x = 40.

14. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50
years, what is definitely the difference between R and Q’s age?

A. 1 year
B. 2 years
C. 25 years
D. Data inadequate
E. None of these
Answer: Option D
Explanation:
Given that: The difference of age b/w R and Q = The difference of age b/w Q and T. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R – Q = ?.
Explanation:
R – Q = Q – T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R – Q) = ?
Here we know the value(age) of Q (25), but we don’t know the age of R.
Therefore, (R-Q) cannot be determined.

15. The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age
will be twice that of his son. The ratio of their present ages is:

A. 5 : 2
B. 7 : 3
C. 9 : 2
D. 13 : 4
Answer: Option B
Explanation:
Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

### Important Formulas on “Problems on Ages”:

If the current age is x, then n times the age is nx.

If the current age is x, then age n years later/hence = x + n.

If the current age is x, then age n years ago = x – n.

The ages in a ratio a : b will be ax and bx.

If the current age is x, then
1/x of the age is x/n.

For more Notes click here.