Problems on Ages
- 1. 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?
Options- A. 32 years
- B. 36 years
- C. 40 years
- D. 48 years Discuss
Correct Answer: 40 years
Explanation:
| Then, the person's present age = | ❨ | 2 | x | ❩ | years. |
| 5 |
| ∴ | ❨ | 2 | x + 8 | ❩ | = | 1 | (x + 8) |
| 5 | 2 |
⟹ 2(2x + 40) = 5(x + 8)
⟹ x = 40.
- 2. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Options- A. 16 years
- B. 18 years
- C. 20 years
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 16 years
Explanation:
| Then, | (6x + 6) + 4 | = | 11 |
| (5x + 6) + 4 | 10 |
⟹ 10(6x + 10) = 11(5x + 10)
⟹ 5x = 10
⟹ x = 2.
∴ Sagar's present age = (5x + 6) = 16 years.
- 3. 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?
Options- A. 1 year
- B. 2 years
- C. 25 years
- D. Data inadequate
- E. None of these Discuss
Correct Answer: Data inadequate
Explanation:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. 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.
- 4. 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?
Options- A. 24
- B. 27
- C. 40
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 24
Explanation:
| 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.
- 5. 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:
Options- A. 5 : 2
- B. 7 : 3
- C. 9 : 2
- D. 13 : 4 Discuss
Correct Answer: 7 : 3
Explanation:
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⟹ 3x + 20 = 2x + 40
⟹ x = 20.
∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
- 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:
Options- A. 14 years
- B. 18 years
- C. 20 years
- D. 22 years Discuss
Correct Answer: 22 years
Explanation:
∴ (x + 24) + 2 = 2(x + 2)
⟹ x + 26 = 2x + 4
⟹ x = 22.
- 7. 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:
Options- A. 14 years
- B. 19 years
- C. 33 years
- D. 38 years Discuss
Correct Answer: 14 years
Explanation:
⟹ 2x = 38.
⟹ x = 19.
∴ Son's age 5 years back (19 - 5) = 14 years.
- 8. At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
Options- A. 12 years
- B. 15 years
- C. 19 and half
- D. 21 years Discuss
Correct Answer: 15 years
Explanation:
4x + 6 = 26 ⟺ 4x = 20
x = 5.
∴ Deepak's age = 3x = 15 years.
- 9. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
Options- A. 16 years
- B. 18 years
- C. 28 years
- D. 24.5 years
- E. None of these Discuss
Correct Answer: 24.5 years
Explanation:
Then, Sachin's age = (x - 7) years.
| ∴ | x - 7 | = | 7 |
| x | 9 |
⟹ 9x - 63 = 7x
⟹ 2x = 63
⟹ x = 31.5
Hence, Sachin's age =(x - 7) = 24.5 years.
- 10. 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?
Options- A. 4 years
- B. 8 years
- C. 10 years
- D. None of these Discuss
Correct Answer: 4 years
Explanation:
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⟹ 5x = 20
⟹ x = 4.
∴ Age of the youngest child = x = 4 years.
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