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- Question
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
- Correct Answer
- 15 years
ExplanationLet the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,4x + 6 = 26 ⟺ 4x = 20
x = 5.
∴ Deepak's age = 3x = 15 years.
Problems on Ages
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- 1. 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:
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.
- 2. 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:
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.
- 3. 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:
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.
- 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:
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.
- 5. 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:
Given that:
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.- 6. 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:
Let Rahul's age be x years.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.
- 7. 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:
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.
- 8. 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).
Options- A. 8, 20, 28
- B. 16, 28, 36
- C. 20, 35, 45
- D. None of these Discuss
Correct Answer: 16, 28, 36
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.
- 9. 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, then how old is B?
Options- A. 7
- B. 8
- C. 9
- D. 10
- E. 11 Discuss
Correct Answer: 10
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.
- 10. 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:
Options- A. 12 years
- B. 14 years
- C. 18 years
- D. 20 years Discuss
Correct Answer: 20 years
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..
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