Problems on Ages

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Practice Questions - Problems on Ages

Age is defined as a period of time that a person has lived or a thing has existed. Problems based on ages generally consist of information of ages of two or more persons and a relation between their ages in present/future/past. Using the information, it is asked to calculate the ages of one or more persons in present/future/past.

Important formulas:

1) If the present age is y, then n times the age is ny.
2) If the present age is y, then age n years later/hence = x + n.
3) If the present age is y, then age n years ago = x – n.
4) The ages in the ratio a:b will be ay, by.
5) If the present age is y, then 1/n of the age is x/n.

Q1) In a family, the average age of father and mother is 35 yr. The average age of the father, mother and their only son is 27 yr. What is the age of the son?
1) 12 yr
2) 11 yr
3) 10.5 yr
4) 10 yr

Solution:

Total age of mother and father = 35(2) = 70 yr
Total age of mother, father and son = 27(3) = 81 yr
Age of son = 81 – 70 = 11 yr

Q2) The difference between the ages of Meena and Seema is 3 yr and the ratio between their ages is 7:8. What is the sum of their ages?
1) 43 yr
2) 41 yr
3) 45 yr
4) 48 yr

Solution:

Let the ages of Meena and Seema be 7y, 8y respectively.
8y – 7y = 3 i.e. y = 3
Sum of their ages = 7y + 8y = 15y = 15(3) = 45 yr

Q3) The ratio of the present age of Manoj to Wasim is 3:11. Wasim is 12 yr younger than Rehana. Rehana’s age after 7 yr will be 85 yr. What is the present age of Manoj’s father, who is 25 yr older than Manoj?
1) 43 yr
2) 67 yr
3) 45 yr
4) 69 yr

Solution:

Let the present age of Manoj and Wasim be 3y, 11y respectively.
11y = 85 – 7 – 12 i.e. y = 6
Present age of Manoj = 3y = 3(6) = 18
Present age of Manoj’s father = 18 + 25 = 43 yr

Q4) The present ages of two persons are 36 and 50 yr, respectively. If after n yr the ratio of their ages will be 3:4, then the value of n is
1) 3
2) 4
3) 7
4) 6

Solution:

According to the question,
(36 + n)/ (50 + n) = 3/4 i.e. 144 + 4n =150 + 3n
n = 6

Q5) The age of a man after 15 yr is 4 times the age of that man 15 yr before. His present age is
1) 10 yr
2) 15 yr
3) 20 yr
4) 25 yr

Solution:

Let the present age of the man be y yr.
According to the question,
y + 15 = 4(y – 15) i.e. 3y = 75
y = 25

Q6) The present age of Ravi’s father is 4 times Ravi’s present age. Five years back, Ravi’s father was 7 times as old as Ravi was at that time. What is the present age of Ravi’s father?
1) 84 yr
2) 70 yr
3) 40 yr
4) 35 yr

Solution:

Let the present age of Ravi be y. Then, the present age of Ravi’s father = 4y
5 yr ago, Ravi’s father age = 7 times Ravi’s age
4y – 5 = 7(y – 5)
On solving, y = 10
Present age of Ravi’s father = 4y = 4(10) = 40 yr