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- Question
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
- Correct Answer
- 20 years
ExplanationLet 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..
Problems on Ages
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- 1. 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.
- 2. 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.
- 3. 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.
- 4. 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.
- 5. 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:
Let 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.
- 6. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
Options- A. 2 times
- B.
2 1 times 2 - C.
2 3 times 4 - D. 3 times Discuss
Correct Answer: 2 times
Explanation:
Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.∴ (4x + 8) = 5 (x + 8) 2 ⟹ 8x + 16 = 5x + 40
⟹ 3x = 24
⟹ x = 8.
Hence, required ratio = (4x + 16) = 48 = 2. (x + 16) 24 - 7. 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?
Options- A. 2 years
- B. 4 years
- C. 6 years
- D. 8 years Discuss
Correct Answer: 6 years
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.
- 8. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Options- A. 0°
- B. 10°
- C. 5°
- D. 20° Discuss
Correct Answer: 10°
Explanation:
Angle traced by hour hand in 13 hrs = ❨ 360 x 13 ❩ ° = 130°. 3 12 3 Angle traced by min. hand in 20 min. = ❨ 360 x 20 ❩ ° = 120°. 60 ∴ Required angle = (130 - 120)° = 10°.
- 9. At what angle the hands of a clock are inclined at 15 minutes past 5?
Options- A.
58 1 ° 2 - B. 64°
- C.
67 1 ° 2 - D.
72 1 ° 2
Discuss
Correct Answer:67 1 ° 2
Explanation:
Angle traced by hour hand in 21 hrs = ❨ 360 x 21 ❩ ° = 157 1 ° 4 12 4 2 Angle traced by min. hand in 15 min. = ❨ 360 x 15 ❩ ° = 90°. 60 ∴ Required angle = ❨ 157 1 ❩ ° - 90° = 67 1 ° 2 2 - 10. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
Options- A.
59 7 min. past 3 12 - B. 4 p.m.
- C.
58 7 min. past 3 11 - D.
2 3 min. past 4 11
Discuss
Correct Answer: 4 p.m.
Explanation:
Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = 37 hrs. 4 3 min. 5 sec. of this clock = 3 min. of the correct clock.
⟹ 37 hrs of this clock = 1 hrs of the correct clock. 720 20 ⟹ 37 hrs of this clock = ❨ 1 x 720 x 37 ❩ hrs of the correct clock. 4 20 37 4 = 9 hrs of the correct clock.
∴ The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
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