Problem on Ages | CSAT Preparation - UPSC PDF Download

Formulas

• 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

Solved Examples

Example 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

Correct Answer is Option (c)
20 + 24 + 8 * 2 = 60/2 = 30

Example 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

Correct Answer is Option (b)
According to Mohan 17th, 18th, or 19th …(i)
According to his sister 19th, 20th, 21st or 22nd …(ii)
From (i) and (ii) => 19th

Example 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

Correct Answer is Option (b)
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

Example 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

Correct Answer is Option (d)
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

Example 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

Correct Answer is Option (d)

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.

Example 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

Correct Answer is Option (c)
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

Example 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

Correct Answer is Option (a)
(A + B) – (B + C) = 12
A – C = 12

Example 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

Correct Answer is Option (a)
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

Example 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

Correct Answer is Option (a)
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

Example 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

Correct Answer is Option (a)
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