Formulas and Quick Tricks for 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/n of the age is x/n
Problems on Ages – Aptitude Questions and Solutions
Q.1: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
A. 18 years
B. 24 years
C. 30 years
D. 36 years
Answer: C. 30 years
Explanation: 20 + 24 + 8 × 2 = 60/2 = 30
Q.2: Mohan correctly remembers that his father's birthday is before 20th January but after 16th January, whereas his sister correctly remembers that their father's birthday is after 18th January but before 23rd January. On which date in January is definitely their father's birthday?
A. 18th
B. 19th
C. 20th
D. Missing data
Answer: B. 19th
Explanation: According to Mohan 17th, 18th, or 19th …(i)
According to his sister 19th, 20th, 21st or 22nd …(ii)
From (i) and (ii) => 19th
Problems on Ages – Basic Concepts, Formulas, Math Tricks, Quantitative Aptitude Questions and Solutions
Q.3: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
A. 35 years
B. 40 years
C. 45 years
D. 55 years
Answer: B. 40 years
Explanation: Sum of the present ages of husband, wife and child = (27 × 3 + 3 × 3) years = 90 years.
Sum of the present ages of wife and child = (20 × 2 + 5 × 2) years = 50 years.
Therefore, Husband's present age = (90 – 50) years = 40 years
Q.4: A is 2 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?
A. 7 years
B. 8 years
C. 9 years
D. 10 years
Answer: D. 10 years
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
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Q.5: The ratio between the school ages of Pratosh and Satheesh is 5:6 respectively. If the ratio between the one-third age of Pratosh and half of Satheesh's age of 5:9, then what is the school age of Satheesh?
A. 25 years
B. 30 years
C. 36 years
D. Cannot be determined
Answer: D. Cannot be determined
Explanation: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.
Then, (1/3 × 5x)/(1/2 × 6x) = 5/9
15 = 15
Thus, Shaan's age cannot be determined.
Q.6: 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 id the mother at present?
A. 32 years
B. 36 years
C. 40 years
D. 48 years
Answer: C. 40 years
Explanation: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
Q.7: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
A. 12
B. 24
C. C is elder than A
D. Data inadequate
Answer: A. 12
Explanation: (A + B) – (B + C) = 12
A – C = 12
Q.8: A father said to his son, 'I was as old as you are at 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: A. 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
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Q.9: A person was asked to state his age in years. His reply was, 'Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am.' What was the age of the person?
A. 18 years
B. 20 years
C. 24 years
D. 32 years
Answer: A. 18 years
Explanation: Let the present age of the person be x years.
Then, 3(x + 3) – 3(x – 3) = x
3x + 9 – 3x + 9 = x
=> x = 18
Q.10: The sum of the ages of a son and father is 56 years after four years the age of the father will be three times that of the son. Their ages respectively are:
A. 12 years, 44 years
B. 16 years, 42 years
C. 16 years, 48 years
D. 18 years, 36 years
Answer: A. 12 years, 44 years
Explanation: Present ages of son and father be x years (56 - x) years
(56 - x + 4) = 3(x + 4) or 4x = 48 or x = 12
Ages are 12 years, 44 years
Q.11: When Rajneesh was born, his father age was 29 years older than his Brother and his Mother was 25 years older than his Sister. If his Brother is 2 years elder than his Sister. After 6 years the average age of the family is 20. Then what is the age of Mother when Rajneesh was born?
A. 26 years
B. 27 years
C. 28 years
D. 29 years
Answer: C. 28 years
Explanation: Sister = x; Brother = x + 2; Father = 29 + x + 2; Mother = 25 + x
Present age: 4x + 58
After 6 years: 4x + 58 + 30 = 4x + 88 => 4x + 88 = 100 => x = 3
Hence, Mother's age = 25 + x => 28 years.
Q.12: The ratio of Present age of Sonu and Monu is 6:7. Sonu is 7 years younger than Veeru. Veeru's age after 8 years will be 51 years. Then what is the difference between the present ages of Sonu and Monu?
A. 4 Years
B. 6 Years
C. 8 Years
D. 10 Years
Answer: B. 6 years
Explanation: Sonu / Monu = 6 / 7
Veeru - Sonu = 7
Veeru + 8 = 51. So, Veeru's present age = 43
So, Sonu = 36 years and Monu = 42 years
Hence, difference between the ages of Sonu and Monu = 42 - 36 = 6 years.
Q.13: In a college, the average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of number of boys to the number of girls in the class is:
A. 2:3
B. 2:5
C. 3:2
D. 3:5
Answer: C. 3:2
Explanation: Let, number of boys = x and number of boys = y
Then, (x × 16.4 + y × 15.4) / x + y = 15.8
=> 16.4x + 15.4y = 15.8x + 15.8y
=> 0.6x = 0.4y
Hence, x:y = 3:2
Q.14: 8 years ago, Sadanand's age was 4/3 times that of Anand. 8 years hence, Sadanand's age will be 6/5 times that of Anand. What is the present age of Sadanand?
A. 25
B. 30
C. 35
D. 40
Answer: D. 40 years
Explanation: Let the present age of Sadanand = x and the present age of Anand = y
Equation 1 => x – 8 = 4/3 (y – 8) and Equation 2 => x + 8 = 6/5 (y + 8)
Equation 1 => 3/4 (x – 8) = y – 8 and Equation 2 => 5/6 (x + 8) = y + 8
y = 3/4 (x – 8) + 8 = 5/6 (x + 8) – 8
10 – 20/3 = 10/12 x – 9/12 x
10/3 = x/12
Hence, age of Sadanand = 40 years.
Q.15: The sum of twice the age of Sooraj and his Father's age is 79. The sum of twice the age of Father and Sooraj's age is 104. The average of Sooraj, his Father and his Mother is 32. Then what is the age of his Mother?
A. 34
B. 35
C. 36
D. 37
Answer: B. 35 years
Explanation: Given, 2S + F = 79 and 2F + S = 104
So, we can get the age of S = 18 and F = 43
Now, it's also given, 18 + 43 + M / 3 = 32
Hence, we can calculate Mother's age = 35 years.