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 ages of Ram and Shyam are in the ratio. 2:1. After five year, the ratio of their ages will be 3:2. Their present ages are

  1. 20 and 10

  2. 10 and 5

  3. 15 and 5

  4. 40 and 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let present ages be 2x and x. After 5 years: (2x+5)/(x+5) = 3/2. Cross-multiplying: 4x+10 = 3x+15, so x = 5. Present ages are 10 and 5 years. Option A (40, 20) and D (20, 10) are proportional but don't satisfy the 5-year condition. Option C's values are not in 2:1 ratio.

Multiple choice

Father is 5 year older than the mother and the mother’s age now is thrice the age of the daughter. The daughter is now 10 year old. What was the age of father when the daughter was born?

  1. 20 years

  2. 15 years

  3. 25 years

  4. 30 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Daughter is 10 years old now. Mother's age = 3 × 10 = 30 years. Father is 5 years older than mother = 35 years now. When daughter was born (10 years ago), father was 35 - 10 = 25 years old. Option A (20 years) would make the current age gap too small.

Multiple choice

Three years ago, the average age of Katara, Kaya and Dazna was 30 years and that of Kaya and Dazna, 7 years ago, was 20 years. What is Katara’s present age?

  1. 46 years

  2. 5 years

  3. 40 years

  4. Cannot be determined

  5. 45 years
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total 3 years ago was 30 × 3 = 90, the present total must be 90 + 9 = 99 years. The total of Kaya and Daznza 7 years ago was 20 × 2 = 40, the present total age of Kaya and Dazna must be 40 + 14 = 54 years. The present age of Katara is 45 years

Multiple choice

Directions: The question below is followed by two statements I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and choose the correct alternative.

What is the mother's present age? I. Present ages of mother and child are in the ratio 5 : 1. II. Four years hence, the ratio of the ages of mother and child will be 17 : 5.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in statement I alone or in statement II alone is sufficient to answer the question.

  4. The data in both the statements I and II is not sufficient to answer the question.

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Combining both the statements, we can find her present age.

Multiple choice

Directions: The question below is followed by two statements I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and choose the correct alternative.

What will be Shyam’s age after 6 years?

I. The ratio of present ages of Ram and Shyam is 4 : 3.

II. Ram is seven years older than Shyam.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in statement I alone or in statement II alone is sufficient to answer the question.

  4. The data in both the statements I and II is not sufficient to answer the question.

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statements I and II alone are not sufficient as we cannot get the exact age. Combining both the statements, we can calculate the age.

Multiple choice statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

.Twelve years hence a man 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 x + 12 = 4 (x - 12)
-3x = - 48 - 12
3x = 60
x = 20 years

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

Present ages of $X\;and\;Y$ are in the ratio $5\,\colon\,6$ respectively. Seven years hence this ratio will become $6\,\colon\,7$ respectively. What is $X's$ present age ?

  1. $35$ years
  2. $42$ years
  3. $49$ years

  4. Can't be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

As per question,
$\frac { x }{ y } =\frac { 5 }{ 6 } $
$6x=5y$
$6x-5y=0$  multiply eq by 6.
$36x-30y=0$  ...eq 1
$\frac { x+7 }{ y+7 } =\frac { 6 }{ 7 } $
$7x+49=6y+42$  
$7x-6y=-7$  ...multiply eq by 5.
$35x-30y=-35$.... eq 2
eq1-eq2
$x=35$
Answer (A) 35 Years


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

Two years ago Sam's age was $\displaystyle 4 \frac{1}{2}$ times the age of his son. Six years ago, his age was twice the square of the age of his son. What is the present age of Sam's son ?

  1. $20$
  2. $10$
  3. $15$
  4. $13$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let $m$ be the age of Sam and $s$ be the age of his son
Then, 2 years ago,
$(m -2) = \dfrac{9}{2} (s-2)$
$2m - 4 = 9s - 18$
$2m = 9s - 14 ...(i)$
$6$ years ago,
$(m - 6) = 2(s- 6)^2$
$\left(\dfrac{9s-14}{2} - 6\right) = 2(s-6)^2$
$9s - 14 - 12 = 4(s^2 - 12s + 36)$
$9s - 26 = 4s^2 - 48s + 144$
$4s^2 - 57s + 170 = 0$
$s = \dfrac{57 \pm \sqrt{529}}{8}$ = $\dfrac{57 \pm 23}{8} = 10, 4.25$
Neglect the 4.25 which is a fraction. 
Hence, age of his son is $10$ years.

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

One year ago, the father was $8$ times as old as his son. Now his age is square of the son's age. Find their present ages.

  1. Present age of father is $36$ years and that of his son is $6$ years.
  2. Present age of father is $49$ years and that of his son is $7$ years.
  3. Present age of father is $64$ years and that of his son is $8$ years.
  4. Present age of father is $25$ years and that of his son is $5$ years.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the present age of the son be $x$.
Let the father's present age be $y$.
One year ago, $y-1=8(x-1)$
$\Rightarrow  y-1=8x-8$
$\Rightarrow  y=8x-7$
Now applying the condition, we get
$(8x-7)=x^{2}$
$\Rightarrow x^{2}-8x+7=0$
$\Rightarrow (x-1)(x-7)=0$
$\Rightarrow x=1$ or $x=7$

Hence, the present age of son is either $1$ year or $7$ years.