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 applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

Five years hence, father's age will be $3$ times the age of his son. Five years ago, father was seven times as old as his son. The age of the son at present is

  1. $10$ years
  2. $15$ years
  3. $20$ years
  4. $40$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let $5$ years ago, the ages of son and father were $x$ and $7x$ years respectively, then 
$\displaystyle 3\left( x+5+5 \right) =7x+5+5$
$\displaystyle \Rightarrow  3x+30=7x+10$
$\displaystyle \Rightarrow  4x=20$
$\displaystyle \Rightarrow  x=5$
Thus, present age of son $= x + 5 = 10$ years

Multiple choice applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

The age of a man is the square of his son's age. A year ago, the man's age was $8$ times the age of his son. What is the present age of the man?

  1. $47\ yr$
  2. $49\ yr$
  3. $36\ yr$
  4. $48\ yr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

let present age of son be $x$

present age of father be ${ x }^{ 2 }$
$1$ year ago
age of son $=x-1$
age of father = ${ x }^{ 2 }$-1
so 
${ x }^{ 2 }-1=8(x-1)$
${ x }^{ 2 }-8x+7=0$
$(x-7)(x-1)=0$
$x=7$
son's age $= 7 years$
man's age = ${ x }^{ 2 }=49$ years

Multiple choice applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Their present ages are 6 years and 12 years.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  Let present age of girl be $2x$.

$\Rightarrow$  Then, age of her sister be $x.$
According to the question,
$\Rightarrow$  $(2x+4)(x+4)=160$
$\Rightarrow$  $2x^2+8x+4x+16=160$
$\Rightarrow$  $2x^2+12x+16-160=0$
$\Rightarrow$  $2x^2+12x-144=0$
$\Rightarrow$  $2(x^2+6x-42)=0$
$\Rightarrow$  $x^2+6x-72=0$
$\Rightarrow$  $x^2+12x-6x-72=0$
$\Rightarrow$  $x(x+12)-6(x+12)=0$
$\Rightarrow$  $(x+12)(x-6)=0$
$\Rightarrow$  $x+12=0$ and $x-6=0$
$\therefore$  $x=-12$ and $x=6$
$\Rightarrow$  Age cannot be negative.
$\therefore$  $x=6$
$\Rightarrow$  $2x=2\times 6=12$
$\therefore$  The present ages of girls are $6\,years$ and $12\,years.$

Multiple choice computer and ms office mathematical methods for economics economics

The age of son and father is in the ratio of 3:7, if the age of the father is 42, the age of the son will be___

  1. 21 years

  2. 24 years

  3. 18 years

  4. 20 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio of son to father is 3:7. If 7 parts equal 42, then 1 part equals 6. Therefore, the son's age (3 parts) is 3 * 6 = 18.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Present ages of Amit and his father are in the ratio 2:5 respectively. Four years hence the ratio of their ages becomes 5:11 respectively. What was the father's age five years ago?

  1. 40 years

  2. 45 years

  3. 30 years

  4. 35 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

 Let the present ages of Amit and his father be 2x and 5x years respectively 
Four years hence 
Amit's Age = ( 2x+ 4) years
Father's age = (5x + 4) years
Given $\displaystyle \frac{2x+4}{5x+4}=\frac{5}{11}\Rightarrow (2x+4)=5(5x+4)$


$\displaystyle \Rightarrow 22x+44=25x+20\Rightarrow 3x=24\Rightarrow x=8$

$\displaystyle \therefore $ Father's present age = ( 5 x 8) years = 40 years Father's age 5 years ago = ( 40 - 5)= 35 years

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The ratio of the present age of Manoj to that of Wasim is $3:11$. Wasim is $12\ yr$ younger than Rehana. Rehanas age after $7\ yr$ will be $85\ yr$. What is thepresent age of Manojs father, who is $25\ yr$ older than Manoj?

  1. $43\ yr$
  2. $67\ yr$
  3. $45\ yr$
  4. $69\ yr$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

 the present age of Wasim $=11x$

 present age of Manoj $=3x$

 present age of Rehana $=11x+12$
 present age of Manoj's father $=3x+25$

 after $7$ years, Rehana's age is $85$ years. 
 $11x+12+7=85$
 $ 11x=66$
 $x=6$
 
age of Manoj's father $=3 \times  6 + 25 = 43$ years. 

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The age of  manoj  after $15$ years is $4$ times the age of that $15$ years before. His present age is 

  1. 10 years

  2. 15 years

  3. 20 years

  4. 25 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of manoj be $x$ years.

According to the question,
$x+15=4(x-15)$
$x+15=4x-60$
$3x=75$
$x=25$ years


Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

At present anil is $1.5$ times of purvis age. $8\ yr$ later, the respective ratio between Anil and Purvis ages will be $25:18$. What is Purvis present age?

  1. $50\ yr$
  2. $28\ yr$
  3. $42\ yr$
  4. $36\ yr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let Present age of Purvis is $x$ then, Age of Anil will be $1.5x$
 After $8 yr$,
                   Age of anil $=1.5x+8$ And Age of Purvis $=x+8$
             $\dfrac{25}{18}=\dfrac{1.5x+8}{x+8}$
                        $x=28$
 So Age of Purvis $=28 yr$
Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Twelve years hence a person will be four times as he was twelve years ago, then his present age is

  1. $20$ years
  2. $25$ years
  3. $28$ years
  4. $30$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let his present age be $x$
According to problem
$\Rightarrow\;x+12=4\;(x-12)$
$\Rightarrow\;-3x=-48-12$
$\Rightarrow\;3x=60$
$\Rightarrow\;x=20$ years.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

A father is at present three as old as his son . Five years back he was four times as old as his son.  Find the age of his son

  1. 12 years

  2. 15 years

  3. 18 years

  4. 20 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Present age of the son is 'x' years his father's age is 3x
Five year ago:
Son's age = x - 5 and father's age = $3x - 5$
$\displaystyle \therefore 3x-5=4(x-5)$ or x = 15

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The age of Vamsi's sister is $4\dfrac { 1 }{ 2 } $ times that of Vamsi, where as his uncle is $30$ years older than him. If the total of their ages is $56$ years, what is the age of Vamsi?

  1. $12$ years
  2. $10$ years
  3. $8$ years
  4. $4$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let the age of Vamsi be $x$.
$\therefore$ age of Vamsi's sister  $=4 \cfrac{1}{2} \times x = \cfrac{9}{2} x$
Age of Vamsi's uncle $= 30 +$ Vamsi's age $= 30 + x$
Given that:-
age of Vamsi's sister $+$ age of Vamsi + age of Vamsi's uncle $= 56$
$\Rightarrow \; x + \cfrac{9}{2} x + 30 + x = 56$
$\Rightarrow \; \cfrac{13}{2} x = 56 - 30$
$\Rightarrow$ $13x = 52$
$\Rightarrow$ $x = 4$
Hence, age of Vamsi is $4$ years.
Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

The average age of three boys is $25$ years and their ages are in the ratio $ 3: 5 : 7$. The age of the youngest boy is

  1. $21$ years
  2. $18$ years
  3. $15$ years
  4. $9$ years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of $3$ boys $= (25 $ $\times$ $3)$ years $=75$ years. 

Ratio of their ages $ = 3 : 5 : 7$.
Age of the youngest $=$ $\displaystyle {\left (75\, \times\, \frac{3}{15} \right )}$ years $= 15$ years

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

The present ages of a father and his son are in the ratio $7 : 3$ and the ratio of their ages will be $2 : 1$ after $10 $ years. Then, the present age of father (in years) is -

  1. $42$
  2. $56$
  3. $70$
  4. $77$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the present ages of father and son be $7x$ and $3x$.

After $10$ years, their ages will be $7x+10$ and $3x+10$.
According to the question, we have
$\dfrac {7x+10}{3x+10}=\dfrac {2}{1}$
$1(7x+10)=2(3x+10)$
$7x+10=6x+20$
$7x-6x=20-10$
$x=10$
Then present age of father is $7x$, i.e. $7\times 10=70$ years.

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

Four years ago, the father's age was three times the age of his son. The total of the age of the father and the son after four years will be $64$ years. What is the father's age at present?

  1. $32$ years
  2. $36$ years
  3. $44$ years
  4. $40$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

fathers present age $= x$ years.

sons present age $= y$ years.  

four years ago, fathers age $=3 \times $ sons age.
$(x-4)=(y-4)\times 3$
$x=3y-8$.....(i) 

after 4 years, fathers age$ +$ sons age $= 64 $
$x+4+y+4=64 $
$x+y=56$.....(ii) 

solve for $x$
$x=3\times 56-3x-8$ 
$4x=160$ 
$x=40$ years  

D is correct.   

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

Five years ago Anjali's age was twice Sarita's age. Five years hence, their ages will be $4 : 3$. Anjali's present age is 

  1. $15$ years
  2. $10$ years
  3. $12$ years
  4. $16$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A and S be current ages. (A-5) = 2(S-5) => A-2S = -5. (A+5)/(S+5) = 4/3 => 3A+15 = 4S+20 => 3A-4S = 5. Solving the system: 2A-4S = -10 and 3A-4S = 5. Subtracting gives A = 15.