Quantitative Aptitude

Problems on Ages

346 Questions

Problems on Ages involve calculating current, past, or future ages using ratios, averages, and simple equations. These questions are a regular feature in the arithmetic section of most competitive exams. Practicing these problems helps improve calculation speed and accuracy for time management during tests.

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Problems on Ages Questions

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

$A$ 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

An old rhyme and problem:

If to my age, there added be,
One half of it and three times three,
Four score and seven my age will be,
How old am I, pray tell me?

  1. $52$ years
  2. $50$ years
  3. $48$ years
  4. $54$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$1$ score $= 20$ years

Let the age be $x$.
Then, $x + \dfrac{1}{2}x + 3\times 3 = 4 \times 20 + 7$
$\Rightarrow  \dfrac{3}{2}x + 9 = 80 + 7$
$\Rightarrow  \dfrac{3}{2}x = 78$
$\Rightarrow  x = 78 \times \dfrac{2}{3}$
$\Rightarrow  x = 52$
Therefore, the age is $52$ years.

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

Three years ago, the average age of the family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. What is the baby today?

  1. 4 years

  2. 3 years

  3. 2 years

  4. 1 year
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Present total ages of six members $=17\times6$ i.e., 102 years.
Present ages of 5 members $=5\times(17+3)$ i.e. 100 years.
$\implies$ Baby is 2 years old to-day.

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, $2x + 3 = 45$
Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

The average age of a family of 6 members 4 years ago was 25 years. Meanwhile a child was born in this family and still the average age of the whole family is same today. The present age of child is ......

  1. 2 years
  2. $1 \displaystyle \frac{1}{2} $ years

  3. 1 years

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of 6 family members four year ago =$25\times 6=150$years
Total age of 6 family member now=150+$4\times 6=150+24=174$years
Total age of 6 family member and child =$25\times 7=175$year
Age of child =175-174=1 year