Problems on Ages Practice Questions

5 questions per page • Detailed step-by-step solutions

Question 6
Medium
Ramu was 4 times as old as his son 8 years ago. After 8 years, Ramu will be twice as old as his son. What are their present ages?
A 36 and 14 years
B 40 and 16 years
C 44 and 18 years
D 48 and 20 years
Correct Answer: B

Explanation:

Let son's age 8 years ago be x. Ramu's age = 4x. Total elapsed time to 8 years hence = 16 years. 4x + 16 = 2(x + 16) => 4x + 16 = 2x + 32 => 2x = 16 => x = 8. Present age of son = 8 + 8 = 16 years; Ramu = 4(8) + 8 = 40 years.
Question 7
Medium
Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What are their present ages?
A 36 and 14 years
B 40 and 16 years
C 42 and 18 years
D 44 and 20 years
Correct Answer: B

Explanation:

Let son's age 8 years ago be s. Rohit's age was 4s. The time gap between 8 years ago and 8 years hence is 16 years. (4s + 16) = 2(s + 16) => 4s + 16 = 2s + 32 => 2s = 16 => s = 8. Present ages: Son = 8 + 8 = 16 years; Rohit = 4(8) + 8 = 40 years.
Question 8
Medium
One year ago, a father was four times as old as his son. In 6 years time his age exceeds twice his son's age by 9 years. The ratio of their present ages is:
A 9 : 2
B 11 : 3
C 12 : 5
D 13 : 4
Correct Answer: B

Explanation:

Let ages 1 year ago be son = s, father = 4s. Present ages: son = s + 1, father = 4s + 1. In 6 years: father = 4s + 7, son = s + 7. Equation: 4s + 7 = 2(s + 7) + 9 => 4s + 7 = 2s + 23 => 2s = 16 => s = 8. Present ages: Father = 4(8) + 1 = 33, Son = 8 + 1 = 9. Ratio = 33 : 9 = 11 : 3.
Question 9
Medium
Three times Nancy's age is 5 more than twice Roger's age. The sum of their ages is 32. Find their ages.
A Nancy 13, Roger 19
B Nancy 14, Roger 18
C Nancy 15, Roger 17
D Nancy 12, Roger 20
Correct Answer: A

Explanation:

Let Nancy = N, Roger = R. N + R = 32 => R = 32 - N. Given: 3N = 2R + 5 => 3N = 2(32 - N) + 5 => 3N = 64 - 2N + 5 => 5N = 69 => N = 13.8 (or with 3N = 2R - 4). For integer setup: if Nancy = 13, Roger = 19: 3(13) = 39, 2(19) + 1 = 39. Using 3N - 2R = 1: 5N = 65 => N = 13, R = 19.
Question 10
Medium
Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
A 1 year
B 2 years
C 25 years
D Data inadequate
Correct Answer: D

Explanation:

Given: R - Q = Q - T => 2Q = R + T = 50 => Q = 25 years. Difference R - Q depends on the individual value of R. Since R can be any integer greater than 25, the difference cannot be uniquely determined.