Problems on Ages
- 1. The total ages of A, B and C at present is 90 years. Ten years ago the ratio of their ages was 1 : 2 : 3. Then the present age of B is ....?
Options- A. 30 years
- B. 20 years
- C. 40 years
- D. None of these Discuss
Correct Answer: 30 years
Explanation:
Let the respective ages of A, B and C, ten years ago be x, 2x and 3x years.
? (x + 10) + (2x + 10) + ( 3x + 10) = 90
? 6x = 60
? x = 10
? B's present age = 2x + 10 = 30 years
- 2. A father's age is four times as much as the sum of the ages of his three children but 6 years hence his age will be only double the sum of their ages. Then the age of the father is?
Options- A. 30 years
- B. 40 years
- C. 60 years
- D. 45 years Discuss
Correct Answer: 60 years
Explanation:
Let father's age be x years and the sum of ages of children be y years.
? x = 4 y ....(i)
Also (x + 6) = 2(y + 6 + 6 + 6) ....(ii) [6 is added thrice for three children ]
Solving (i) and (ii)
x = 60 years, and y = 15 years.
- 3. In ten years, A will be twice as old as B was 10 years ago. If A is now 9 years older then B. Find the present age of B?
Options- A. 39 year
- B. 40 year
- C. 36 year
- D. 49 year Discuss
Correct Answer: 39 year
Explanation:
Let B's present age be x years then A's present age be (x + 9) years
As per the given condition
(x + 9 + 10) = 2(x - 10)
? x = 39
? The present age of B = 39 years
- 4. Present age of Rahul is 8 years less then Ritu's present age. If three years ago Ritu's age was x, which of the following represents Rahul's present age?
Options- A. x + 3
- B. x - 5
- C. x - 3 + 8
- D. x + 3 + 8 Discuss
Correct Answer: x - 5
Explanation:
Let the Rahul's present age is 'A' years. Then Ritu's present age is (A + 8)
Now, according to the question,
(A + 8) - 3 = x
? A = (x - 5) years
- 5. The ratio in the present ages of Ramesh and Jayesh is 3 : 2. four years ago Ramesh's age was more then Jayesh's age by 6 years. What is the present age of Jayesh?
Options- A. 18 years
- B. 12 years
- C. 6 years
- D. Data is inadequate Discuss
Correct Answer: 12 years
Explanation:
Let the present age of Ramesh be 3x years and the present age of jayesh = 2x years.
According to question, (3x - 4) = (2x - 4) + 6
? 3x - 4 = 2x - 4 + 6
? 3x - 4 = 2x + 2
? 3x - 2x = 2 + 4
? x = 6
? Present age of Jayesh = 2x = 12 years
- 6. The age of the father 4 years ago was 5 times the age of his son. If the sum of their present ages is 44 years. What is the present age of his son?
Options- A. 6 years
- B. 10 years
- C. 4 years
- D. 8 years Discuss
Correct Answer: 10 years
Explanation:
Let the present age of father and son be x and y years respectively.
From 1st condition,
(x - 4) = 5(y- 4)
? x - 4 = 5y - 20
? x - 5y = -16 .....(i)
From 2nd condition,
? x + y = 44 ...(ii)
From equation (i) and (ii)
-6y = -60
? y = 10
? Present age of son = 10 years
- 7. The ratio in the ages of A and B, 1 year ago was 3 : 4. While it will be 5 : 6 after 1 year. What is the present age of B?
Options- A. 8 years
- B. 4 years
- C. 6 years
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Let the present age of A and B be x and y years respectively
From 1st condition
(x - 1) / (y -1) = 3/4
? 4x - 4 = 3y - 3
? 4x - 3y = 1 ... (i)
From 2nd condition,
(x + 1) / (y + 1) = 5/6
? 6x + 6 = 5y + 5
? 6x - 5y = -1 ...(ii)
Multiplying equation (i) by 3 and equation (ii) by 2 and subtract
y = 5
? Present age of B = 5 years
- 8. The sum of the ages of Yogesh, Prakash and sameer is 93 years. 10 years ago the ratio of their ages was 2 : 3 : 4. What is the present age of sameer?
Options- A. 32 years
- B. 24 years
- C. 34 years
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Let the respective ages of Yogesh, Prakash, and Sameer 10 years's ago be 2x, 3x and 4 x years.
? Present age of Yogesh = (2x + 10 ) years
? Present age of Prakash = (3x + 10 ) years
? Present age of sameer = (4x + 10) years
According to question,
(2x + 10) + (3x + 10) + (4x + 10 ) = 93
? 9x + 30 = 93
? 9x = 63
? x = 7
? Present age of Sameer = 4x + 10 = 28 + 10 = 38 years .
- 9. A man is five times as old as his son. four years later the sum of their ages will be 56 years. How old is the son at present?
Options- A. 12 years
- B. 5 years
- C. 6 years
- D. 8 years Discuss
Correct Answer: 8 years
Explanation:
Let the present age of man be x years and the age of his son be y years.
From 1st condition,
x = 5y .....(i)
From 2nd condition ,
(x + 4 ) + (y + 4) = 56
? x + y + 8 = 56
? x + y = 48 ... (ii)
Putting x = 5y in equation (ii)
5y + y = 48
? 6y = 48
? y = 8
? Age of son = 8 years
- 10. If A son is younger then his father by 25 years and the father was 45 years old,4 years ago. What will be the total age of the father and son after 5 years?
Options- A. 82 years
- B. 88 years
- C. 83 years
- D. 78 years Discuss
Correct Answer: 83 years
Explanation:
Let the present age of father be x years, Then the present age of son = (x - 25) years .
According to to question,
x - 4 = 45
? x = 45 + 4
? x = 49
? Age of son = 49 - 25 = 24 years
? Age of son after five years = 24 + 5 = 29 years
? Age of father after five years = 49 + 5= 54 years
Total age of both = 29 + 54= 83 years
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