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 maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of mother is excluded. How old is the mother?

  1. 40 years

  2. 42 years

  3. 48 years

  4. 50 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The average age of the mother and her 6 children (7 people total) is 12 years, meaning their total age is 7 * 12 = 84 years. When the mother is excluded, the average of the 6 children drops by 5 years to 12 - 5 = 7 years, making the total age of the children 6 * 7 = 42 years. Subtracting the children's total age from the family's total age gives the mother's age as 84 - 42 = 42 years.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Two years ago, a father was five times as old as his son. Two years later, father age will be 8 more than three times the age of the son. Find the sum of present ages of father and son.

  1. 62 years

  2. 52 years

  3. 42 years

  4. 34 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let F and S be the present ages of the father and son. Two years ago, F - 2 = 5(S - 2), which simplifies to F - 5S = -8. Two years later, F + 2 = 3(S + 2) + 8, which simplifies to F - 3S = 12. Solving these simultaneous equations gives S = 10 and F = 42, so the sum of their present ages is 42 + 10 = 52 years.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

After $12$ years I shall be $3$ times as old as I was $4$ years ago. Find my present age.

  1. $12$
  2. $13$
  3. $14$
  4. $15$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let my present age$=x$ years

After $12$ years my age$=x+12$ years

$4$ years ago my age $=x-4$ years

According to the question,

$x+12=3\left(x-4\right)$

$\Rightarrow x+12=3x-12$

$\Rightarrow 3x-x=12+12$

$\Rightarrow 2x=24$ or $x=\dfrac{24}{2}=12$ years.

$\therefore$ my present age is $12$ years.
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

20 years ago when my parents got married their average age was 23 years, now the average age of my family consisting of my self and my parents is 34 years, then my present age is?

  1. 14 years

  2. 16 years

  3. 18 years

  4. 36 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

20 years ago, the average age of the parents was 23, so their total age then was 46. Today, 20 years later, the sum of their present ages is 46 + 2 * 20 = 86 years. The current average age of the family of three (parents + child) is 34, meaning the total family age is 3 * 34 = 102 years. Subtracting the parents' total age from the family total gives the child's present age as 102 - 86 = 16 years.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

If  $12$  years hence of Ravi will he  $9$  times his age  $12$  years ago, find the present age of Ravi

  1. $12 years$
  2. $15 years$
  3. $18 years$
  4. $20 years$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Ravi's present age be R. 12 years hence, his age will be R + 12, and 12 years ago, his age was R - 12. According to the problem, R + 12 = 9(R - 12). Expanding this gives R + 12 = 9R - 108, which simplifies to 8R = 120, resulting in R = 15 years.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

$A$  is  $3$ times as old as  $B$  and  $C$  together. If after  $10$  years  $A's$  age would be equal sum of the ages of  $B$  and  $C .$  find the present age of  $A$

  1. $15$ years
  2. $20$ years
  3. $21$ years
  4. $25$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A = 3(B + C). After 10 years, (A + 10) = (B + 10) + (C + 10). A + 10 = B + C + 20, so A = B + C + 10. Substituting B + C = A/3, we get A = A/3 + 10. 2A/3 = 10, so A = 15.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The present age of Sohan is $20$ years more than the present age of Sachin. $3$ years hence, it will be thrice that of Sachin. Find the present age of Sohan.

  1. $23$ years
  2. $27$ years
  3. $30$ years
  4. $37$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Sachin's present age be S. Sohan's present age is S + 20. 3 years hence, Sohan's age will be S + 23 and Sachin's age will be S + 3. We are given S + 23 = 3(S + 3), which expands to S + 23 = 3S + 9, resulting in 2S = 14 and S = 7. Therefore, Sohan's present age is 7 + 20 = 27 years.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

$A$ is older than $B$. Taking present ages of $A$ and $B$ as $x$ years and $y$ years respectively, find in terms of $x$ and $y$. The difference between the ages of A and B.

  1. $(2x - y) years$
  2. $(x - 3y) years$
  3. $(x - y) years$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given, 
$A$ is older than $B$. Taking present ages of $A$ and $B$ as $x$ years and $y$ years respectively.
The difference between the ages of A and B.

$ = (x - y) $

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

To find the present age of Rishi, which statements can be dispensed.
I. In ten years,Richard will be twice as old as Rishi was 10 years ago.
II. Richard is now 9 years older than Rishi.
III. Five years ago, Rishi was 9 years younger than Richard.

  1. Only II

  2. Only III

  3. Either I or II

  4. None of the three statements can be dispensed with
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
There are 2 unkown variables, Rishi's age x and Richard's age y.
Each of the following statements give relation between x and y.

Statement I  says: $\quad y+10=2x.$
Statement II says: $\quad y=x+9$

Statement III says:  $y-5=(x-5)+9$= Statement II.
To solve for 2 unknown we require 2 equations.

Since, Statement II and Statement III are equivalent , either can be dispensed with.
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Ajit is $21$ years younger than his father. What is their total age in $7$ years time?

  1. $(x + 28)$ years
  2. $(x + 35)$ years
  3. $(2x + 28)$ years
  4. $(2x + 35)$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let the age of Ajit be $x$ years.
$\therefore$ Age of Ajit's father $= x + 21$
After $7$ years-
Age of Ajit $= (x + 7)$ years
Age of Ajit's father $= x + 21 + 7 = x + 28$
Total age of Ajit and Ajit' father $= x + 7 + x + 28 = (2x + 35)$ years
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Ram's father's age is 3 years more than two times Ram's age. Ram's father is 45 years old. Form an equation to find Ram's age.

  1. 2x + 3 = 45

  2. 3x + 2 = 45

  3. 6x + 3 = 45

  4. 5x + 1 = 45
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
 Let Ram's age be $x$ years.
$\Rightarrow$  Ram's father's age = $(2x + 3)$ years
$\therefore$    According to question, $2x + 3 = 45$