Quantitative Aptitude

Problems on Ages

1,744 Questions
All Translate multiples, fractions, and percentages 518 Use two ratios from different dates 500 Convert an age ratio into actual ages 258 Handle averages and changing groups 167 Generational age chains 111 Recognize equal age gaps 101 Product of ages 68 Ages in arithmetic progression 11 Division of lifespan 9

Problems on Ages Questions

Multiple choice

The age of Sarthak is one-fifth of the age of his mother and the sum of the ages of the son and the mother is equal to the age of the father. After $15$ years, the sum of the ages of the son and his mother will be four-third of his fathers age. Find the ratio of the present ages of Sarthak, mother and father respectively.
  1. $1 : 5 : 7$
  2. $2 : 10 : 10$
  3. $1 : 5 : 6$
  4. $2 : 8 : 9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let S, M, F be current ages. S = M/5, S+M = F. So F = M/5 + M = 6M/5. After 15 years: (S+15) + (M+15) = 4/3(F+15). Substitute S=M/5 and F=6M/5: (M/5 + M + 30) = 4/3(6M/5 + 15). 6M/5 + 30 = 8M/5 + 20. 10 = 2M/5, so M = 25. Then S = 5, F = 30. Ratio S:M:F = 5:25:30 = 1:5:6.

Multiple choice

$X$ is three times as old as $Y, Z$ was twice as old as $x$ four years ago. In the four year time, $x$ will be of $31$ years. What is the present age of $y$ and $z$.
  1. $9$ years, $46$ years
  2. $9$ years, $50$ years
  3. $10$ years, $46$ years
  4. $10$ years, $50$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since X will be 31 in four years, X is currently 27. As X is three times Y, Y is 9 years old. Four years ago Z was twice X's age then, so Z - 4 = 2(27 - 4), giving Z = 50.

Multiple choice

Ten years ago, average of the ages of a men and his wife was 25 years. Today the average age of these two and their son, taken together is again 25 years. What is the age (in years) of the son today?
  1. $2$
  2. $5$
  3. $8$
  4. $10$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ten years ago, the sum of the ages of the man and wife was 25 * 2 = 50. Today, their combined age is 50 + 10 + 10 = 70. The current average age of the three is 25, so the sum of their ages is 25 * 3 = 75. The son's age is 75 - 70 = 5.

Multiple choice

The age of the father of two children is twice that of the elder one added to four times that of the younger one. If the geometric mean of the ages of the children is $4\sqrt 3 $ and their harmonic mean is 6, then father's age is

  1. 36

  2. 40

  3. 50

  4. 56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let ages be x and y. Geometric mean sqrt(xy) = 4*sqrt(3) => xy = 48. Harmonic mean 2xy/(x+y) = 6 => 2(48)/(x+y) = 6 => x+y = 16. Solving x+y=16 and xy=48 gives x=12, y=4. Father's age = 2(12) + 4(4) = 24 + 16 = 40.

Multiple choice

A woman is 30 years older than her son. Fifteen years ago, she was twice as old as her son. Find their present ages.

  1. Age of woman = 75 years, Age of son = 35 years

  2. Age of woman = 45 years, Age of son = 25 years

  3. Age of woman = 85 years, Age of son = 35 years

  4. Age of woman = 75 years, Age of son = 45 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let son's age be x, woman's age be x + 30. 15 years ago: (x + 30 - 15) = 2 * (x - 15). x + 15 = 2x - 30. x = 45. Woman is 45 + 30 = 75. Option D matches these values.

Multiple choice

Directions: Compare the two quantities in A and B. The averages of a husband, his wife and son three years ago was 27 years and that of his wife and son five years ago was 20 years. Quantity A Quantity B Husband`s present age 40

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let H, W, S be current ages. (H-3 + W-3 + S-3)/3 = 27 => H+W+S = 90. (W-5 + S-5)/2 = 20 => W+S = 50. Thus, H = 90 - 50 = 40. Quantity A is 40, Quantity B is 40. They are equal.