# Problems on Ages Practice Set – 1

Problems on Ages Practice Set – 1
1. The sum of the present ages of a father and his son is 60 years. Five years ago, father's age was four times the age of the son. so now the son's age will be:
a) 5
b) 10
c) 15
d) 20
e) 25
Explanation: Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 5= 4(x - 5)
55 - x = 4x – 20
5x = 75 => x = 15

2. Sivagami is 2 years elder than Avanthika. After 6 years the total of their ages will be 7 times of their current age. Then age of Sivagami is :
a) 19 years
b) 17 years
c) 15 years
e) None of these
Explanation: Let Avanthika’s age = A.
Then Sivagami’s age = A + 2
After 6 years the total of their ages will be 7 times of what?
Not clear.
So the given data are inadequate.

3. The age of a person is thrice the total ages of his 2 daughters. 0.5 decades hence, his age will be twice of the total ages of his daughters. Then what is the father’s current age? [0.5 Decades = 5 Years]
a) 35 years
b) 40 years
c) 45 years
d) 47 years
e) 50 years
Explanation: Let, Total of current ages of the 2 daughters is A years.
Then, father’s current age = 3A years.
(3A + 5) = 2 (A +10)
3A + 5 = 2A + 20
A = 15
Therefore, father’s current age = 45 years.

4. The ages of X and Y are in the proportion of 6:5 and total of their ages is 44 years. The proportion of their ages after 8 years will be
a) 3 : 6
b) 6 : 3
c) 8 : 7
d) 9 : 5
e) 9 : 7
Explanation: Let current ages of X and Y correspondingly, is 6A & 5A
Given: 6A + 5A = 44
=> A = 4
Proportion of ages after 8 years will be
6A + 8 : 5A + 8 => 32:28 (or) 8:7

5. The ages of Krish and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is:
a) 10
b) 13
c) 15
d) 18
e) 20
Explanation: Krish’s age = 3A and Vaibhav’s age = 5A
(3A + 9)/(5A + 9) = 3/4
=> 4 (3A + 9) = 3 (5A + 9)
=> A = 3
Therefore, Vaibhav’s age = 15 years.

6. The ratio between the present ages of P and Q is 6 : 7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years ?
a) 3 : 4
b) 3 : 5
c) 4 : 3
d) 7 : 8
e) None of these
Explanation: Let P's age and Q's age be 6x years and 7x years respectively.
Then, 7x - 6x = 4 <=> x = 4.
Required ratio = (6x + 4) : (7x + 4) = 28 : 32 = 7 : 8.

7. The average age of a couple is 24 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child ?
a) 2 years
b) 3 years
c) 4 years
d) 5 years
e) 6 years
Explanation: 29 x 2 = 58
20 x 3 = 60
The present age of the child = 60 – 58 = 2 years
Therefore, the age of child is 2 years.

8. The average age of seven persons sitting in a row facing east is 26 years. If the average age of the first three persons is 19 years and the average age of the last three persons is 32 years, then find the age of the person sitting in the middle of the row ?
a) 32 years
b) 29 years
c) 24 years
d) 27 years
e) 33 years
Explanation: Total age seven persons = (26 x 7)years
Total age of the first three persons and the last three persons are (19 x 3) years and (32 x 3) years respectively.
Age of the person sitting in the middle of the row = 26 x 7 - 19 x 3 - 32 x 3 = 182 - 57 - 96 = 29 years.

9. Ratio of the ages of Mahesh and Nilesh is 5 : x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x ?
a) 11.8
b) 12.9
c) 13.7
d) 14.5
e) 15.6
Explanation: Let the present ages of Mahesh, Nilesh and Ramesh be k, l and m respectively.
k/l = 5/x ------ (1)
k = m - 18 ------ (2)
m + 9 = 47 ------ (3)
k - l = m ----- (4)
(3) => m = 47 - 9 = 38 years
(2) => k = 38 -18 = 20 years
(1) => 20/l = 5/x => l = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5

10. Raju got married 8years ago. His present age is 6/5 times his age at the time of his marriage Raju's sister was 10years younger to him at the time of his marriage. The present age of Raju's sister is  ?
a) 30
b) 32
c) 36
d) 38
e) None of these