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 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

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

The ratio of the present ages of two brothers is $1:2$ and $5$ years back the ratio was $1:3$. What will be the ratio of their ages after $5$ years?

  1. $1:4$
  2. $2:3$
  3. $3:5$
  4. $5:6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the age of the two brothers be $x$ and $y$ respectively


Given


At present 

$\dfrac { x }{ y } =\dfrac { 1 }{ 2 } \Rightarrow y=2x$

Five years ago

$\dfrac { x-5 }{ y-5 } =\dfrac { 1 }{ 3 }$

substitute $y=2x$ 

$\dfrac { x-5 }{ 2x-5 } =\dfrac { 1 }{ 3 }$

$\Rightarrow 3x-15=2x-5\Rightarrow x=10$

$\Rightarrow y=2x=2(10)=20$

$\therefore\ x=10$ and $y=20$

Required ratio:

$\displaystyle \frac { x+5 }{ y+5 } =\frac { 10+5 }{ 20+5 } =\frac { 15 }{ 25 } =\frac { 3 }{ 5 }$

Hence option (C) is the correct option.

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

The ratio between the ages of $A$ and $B$ is $2 : 5$. After $8$ years, their ages will be in the ratio $1 : 2$. What is the difference between their present ages?

  1. $20$ years
  2. $22$ years
  3. $24$ years
  4. $25$ years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let $A = 2x; B = 5x$ be the present ages of $A$ and $B$ respectively.
After $8$ years, their ages will be $(2x + 8)$ years and $(5x + 8)$ years respectively.
Therefore, $ (2x + 8) : (5x + 8) : : 1 : 2$
$\Rightarrow  (5x + 8)\times 1 = 2(2x + 8)$
$\Rightarrow x = 8$
Thus difference of their present ages is $5x - 2x = 3x$ i.e., $24$ years.

Multiple choice time speed and distance problems involving speed word problems on speed time and distance time and distance word problems on simultaneous equations applications of simultameous equations unitary method idea of speed distance and time speed math time work and distance ratio and proportions linear equations in two variables maths

The present ages of Reena and Usha ar 24 and 36 yr respectively. What was the ratio between the ages of Usha and Reena respectively 8 yr ago?

  1. 7:4

  2. 4:7

  3. 11:8

  4. 8:11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Age of Reena after 8yr=24−8=16yr
Age of Usha After 8yr=36−8=28
So, the ratio will be 1628=47

Multiple choice

The present ages of A and B are in the ratio 2 : 3 and the ages of A and C are in the ratio 3 : 4. If the sum of the present ages of A, B and C is 92 years, how many years will it take to get the ages of B and C in the ratio 10 : 9?

  1. 2 years

  2. 4 years

  3. 6 years

  4. 8 years

  5. 10 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A:B = 2:3, A:C = 3:4. A:B:C = 6:9:8. Sum of parts = 23. 23x = 92, so x = 4. Ages: A=24, B=36, C=32. After t years, (36+t)/(32+t) = 10/9. 9(36+t) = 10(32+t). 324 + 9t = 320 + 10t. t = 4.

Multiple choice

There is a father, a mother and 2 sons in a family and their total age is 60 years. The difference between the sons' age is 3 years, mother's age exceeds the sum of the sons' age by 17 years and the difference of age of father and mother is equal to the age of the elder son. How old is the father?

  1. 29 years

  2. 24 years

  3. 22 years

  4. 28 years

  5. 30 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sons be x and y (x > y). x - y = 3, so x = y + 3. Mother = (x + y) + 17. Father = Mother + x = (x + y + 17) + x = 2x + y + 17. Total = Father + Mother + x + y = (2x + y + 17) + (x + y + 17) + x + y = 4x + 3y + 34 = 60. Substituting y = x - 3: 4x + 3(x - 3) + 34 = 60, so 7x + 25 = 60, 7x = 35, x = 5. Father = 2(5) + (5-3) + 17 = 10 + 2 + 17 = 29.

Multiple choice

On the occasion of birthday of Mrs. Paul's daughter, Mrs. Paul told her daughter, "4x years ago, I was 4 times your age and my age was 2 times your age 2x years ago." Which of the following can be the age of Mrs. Paul at present, if the difference in the present ages of mother and daughter is 18?

  1. 42 years

  2. 44 years

  3. 46 years

  4. 48 years

  5. 60 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M and D be present ages. M - D = 18. From the first condition: M - 4x = 4(D - 4x) which simplifies to M = 4D - 12x. From the second: M - 2x = 2(D - 2x) which simplifies to M = 2D - 2x. Equating the two expressions for M: 4D - 12x = 2D - 2x, so 2D = 10x or D = 5x. Substituting into M - D = 18 gives M - 5x = 18. Since M = 2D - 2x = 2(5x) - 2x = 8x, we have 8x - 5x = 18, so 3x = 18, x = 6. Thus M = 8(6) = 48.

Multiple choice

The ratio of present age of two persons, Ryan and Simon is 5 : 8. Which of the following can be the ratio of ages of Ryan and Simon after 12 years?

  1. 1 : 2

  2. 3 : 7

  3. 7 : 9

  4. 9 : 19

  5. 9 : 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages be 5x and 8x. After 12 years, the ratio is (5x+12)/(8x+12). Testing the options, for 7:9, (5x+12)/(8x+12) = 7/9 leads to 45x + 108 = 56x + 84, so 11x = 24, which is not an integer. However, checking the ratio 7:9 against the options, it is the only one that could potentially result from an age progression.

Multiple choice

The ratio of the age of Rock to that of Pock is known to be 6 : 5. Which of the following can be the possible ratio of the age of Rock to that of Pock 10 years from now?

  1. 9 : 7

  2. 17 : 11

  3. 19 : 14

  4. 23 : 21

  5. 37 : 27
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let ages be 6k and 5k. After 10 years, the ratio is (6k+10)/(5k+10). Testing options: for 23:21, (6k+10)/(5k+10) = 23/21 leads to 126k + 210 = 115k + 230, so 11k = 20, k = 20/11. Since k must be a positive number, this is a possible ratio.

Multiple choice

A man had three daughters who celebrated their birthday on the same day, but were born in 1977, 1978 and 1979. On one such birthday, if the product of their ages was divided by their respective ages in turn, the sum of quotients would have been 74. Find the age of the eldest daughter (in years).

  1. 6

  2. 8

  3. 9

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let ages be x, x+1, x+2. Product P = x(x+1)(x+2). Sum of quotients = P/x + P/(x+1) + P/(x+2) = (x+1)(x+2) + x(x+2) + x(x+1) = 74. x^2+3x+2 + x^2+2x + x^2+x = 74 => 3x^2 + 6x - 72 = 0 => x^2 + 2x - 24 = 0 => (x+6)(x-4) = 0. x = 4. Eldest is 4+2 = 6.

Multiple choice

If 6 years ago, the ratio of ages of A and B was 10 : 7 and 9 years hence, the ratio will be 13 : 10, then their respective present ages are

  1. 56 years and 41 years

  2. 50 years and 35 years

  3. 39 years and 30 years

  4. 56 years and 31 years

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let ages 6 years ago be 10x and 7x. Present ages are 10x+6 and 7x+6. Nine years hence, ages are 10x+15 and 7x+15. Ratio (10x+15)/(7x+15) = 13/10. 100x+150 = 91x+195, so 9x=45, x=5. Present ages: 10(5)+6=56 and 7(5)+6=41.