Aptitude - Problems On Ages

5 years ago the average age of 4 members was 46 years. A new person joins them now and the average age of all the five members is 50 years. Then the age of new member is

A.  42 years

B.  44 years

C.  46 years

D.  48 years

46 years

Explanation :

Let Fifth person age be x years

Five years ago the average of first 4 persons was 46

Five years ago, the average of first four person = 46

The present average will be 5 years more i.e.

Present average of first 4 persons will be = 46 + 5 = 51

A new person joins then now, and then the average becomes 50

=> [ 4 (51) + x ] / 5 = 50

=> x = 46

Hence, Fifth person's age is x = 46 years

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?

A.  9 years

B.  10 years

C.  11 years

D.  12 years

10 years

Explanation :

Assume the Current age of C be x

=> B's age = 2x, A's age = 2x + 2

=> ( 2x + 2 ) + ( 2x ) + x = 27

=> x = 5

Hence, B's age is 2x = 10 years

Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

A.  14 years

B.  15 years

C.  16 years

D.  17 years

16 years

Explanation :

Let us assume, Six year ago, Kunal's age as 6x and Sagar's age as 5x

Current age of Kunal is 6x+6 and of Sagar is 5x+6

After four years their ages will be in 11 : 10 ratios

( 6x + 6 + 4 ) : ( 5x + 6 + 4 ) = 11 : 10

=> 10 ( 6x + 6 + 4 ) = 11 ( 5x + 6 + 4 )

=> x = 2

=> Sagar's present age = ( 5x + 6 ) = 16 years

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

A.  2 years

B.  3 years

C.  4 years

D.  5 years

4 years

Explanation :

Let the Current age of a youngest child be x years

The sum of all 5 childrens age is 50

( x + 12 ) + ( x + 9 ) + ( x + 6 ) + ( x + 3 ) + x = 50

=> x = 4

Age of the youngest child is x = 4 years

Phil is Jack's father and Phil is 35 years old. Three years ago, Phil was four times as old as his son was then, How old is Jack now?

A.  10 years

B.  11 years

C.  12 years

D.  13 years

11 years

Explanation :

Let the Current age of Jack be x years

Three years ago, Phil's age was 35 - 3 = 32 years

Three years ago, Phil's age was 4 times of Jack's age.

So Phil's age can be represented as 32 = 4 ( x  - 3 ) => x = 11

So, the Current age of Jack is 11 years

John is 20 years younger than Tom. In two years Tom will be twice as old as John. How old are they now?

A.  36, 16

B.  26, 16

C.  36, 26

D.  16, 46

36, 16

Explanation :

Let Current age of Tom be x. Then Current age of John = x - 20

After two years, John's age = ( ( x - 20 ) + 2 ) and Tom's age = x + 2

After two years, Tom will be twice as old as John

So, 2 ( ( x - 20 ) + 2 ) = ( x + 2 )

=> x = 38

Hence, Tom's age is 38 years in 2 years

So, the current age of Tom = (38 - 2) = 36

So, the current age of John = (36 - 20) = 16

Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

A.  2 times

B.  2 (1/2) times

C.  2 (3/4) times

D.  3 times

2 times

Explanation :

Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years

=> (4x+8) = (5/2) (x+8)

=> 8x+16 = 5x+40

=> x = 8

=> Required ratio = (4x+16) / (x+16) = 48/24 = 2

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

A.  14 years

B.  18 years

C.  22 years

D.  24 years

14 years

Explanation :

Let the son's present age be x years

Then (38-x) = x

=> 2x = 38

=> x = 19

=> Son's age 5 years back = (19-5) = 14 years

Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

A.  14

B.  24

C.  34

D.  44

24

Explanation :

Let the present ages of Sameer and Anand be 5x years and 4x years respectively

Then, (5x+3) / (4x+3) = 11 / 9

=> 9 (5x+3) = 11 (4x+3)

=> x = 6

=> Anand's present age = 4x = 24 years

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

A.  16 years

B.  18 years

C.  20 years

D.  22 years

22 years

Explanation :

Let the son's present age be x years. Then, man's present age = (x+24) years

=> (x+24) + 2 = 2 (x+2)

=> x + 26 = 2x + 4

=> x = 22

The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

A.  10

B.  15

C.  20

D.  25

20

Explanation :

Let the present ages of son and father be x and (60-x) years respectively

Then, (60-x) - 6 = 5 (x-6)

=> 54 - x = 5x - 30

=> x = 14

=> Son's age after 6 years = (x+6) = 20 years

At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?

A.  12 years

B.  15 years

C.  18 years

D.  21 years

15 years

Explanation :

Let the present ages of Arun and Deepak be 4x years and 3x years respectively

Then, 4x + 6 = 26

=> x = 5

=> Deepak's age = 3x = 15 years

Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

A.  16.5 years

B.  18.5 years

C.  28.5 years

D.  24.5 years

24.5 years

Explanation :

Let Rahul's age be x years

Then, Sachin's age = (x-7) years

=> (x-7) / x = 7 / 9

=> x = 31.5

=> Sachin's age = (x-7) = 24.5 years

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)

A.  8, 20, 28

B.  16, 28, 36

C.  20, 35, 45

D.  24, 42, 54

16, 28, 36

Explanation :

Let their present ages be 4x, 7x and 9x years respectively

Then, (4x-8) + (7x-8) + (9x-8) = 56

=> 20x = 80

=> x = 4

=> Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively

Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

A.  2 years

B.  4 years

C.  6 years

D.  8 years

6 years

Explanation :

Mother's age when Ayesha's brother was born = 36 years

Father's age when Ayesha's brother was born = (38 + 4) years = 42 years

=> Required difference = (42 - 36) years = 6 years

A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

A.  32 years

B.  36 years

C.  40 years

D.  44 years

40 years

Explanation :

Let the mother's present age be x years

Then, the person's present age = (2x/5) years

=> (2x/5) + 8 = (1/2) (x+8)

=> x = 40

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

A.  1 year

B.  2 years

C.  3 years

Explanation :

Given that:

1. The difference of age b/w R and Q = The difference of age b/w Q and T.

2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question: R - Q = ?.

Explanation:

R - Q = Q - T

(R + T) = 2Q

Now given that, (R + T) = 50

So, 50 = 2Q and therefore Q = 25.

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

Therefore, (R-Q) cannot be determined

The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:

A.  5 : 2

B.  7 : 3

C.  9 : 2

D.  13 : 4

7 : 3

Explanation :

Let the ages of father and son 10 years ago be 3x and x years respectively

Then, (3x+10) + 10 = 2 [(x+10) + 10]

=> 3x + 20 = 2x +40

=> x = 20

=> Required ratio = (3x+10 : (x+10)

=> 70 : 30 = 7 : 3