Problems on Ages- Aptitude Questions and Answers

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The average age of all the 16 professors of L.K. University is 52 years. After four years what will be the average age of all the 16 professors if there is no retirement or recruitment?

A)
68 years

B)
58 years

C)
56 years

D)
None of these


Correct Answer :

56 years


Explanation :

total age of 16 professors => 52 years * 16 professors => 832 years
after 4 years total age would be 832 years (16professors * 4 years)= 896 years

Then Average age would be After four years => 896/16 => 56 years

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Three years ago, X’s age was 2 times as that of Y’s. Seven years hence, the sum of their ages will be 83 years. What is the age of X today?

A)
47 years

B)
35 years

C)
45 years

D)
26 years


Correct Answer :

45 years


Explanation :

As given three years ago, Xs age was 2 times as that of Ys then (x-3) = 2(y-3)
x = 2y-3 ------------------eq1
The sum of their ages will be 83 years, then (x+7) + (y+7) = 83
x+y = 69------------------eq2

After substitute the value of x from eq1 to eq2.
(2y-3) + y = 69
3y - 3 = 69
3y = 72
y = 24

If y is 24, then substitute the value of y in eq2
x+y = 69
x=69-24
x=45

10 years ago, the average age of a family of 5 members was 25 years. In the last 10 years 2 children were born in the family. The family now has 7 members. If the present average age of the family is 27 years, then what is the age of the elder child if it is known that the elder child is 4 years older to the younger one?

A)
7 years

B)
18 years

C)
9 years

D)
Can’t be determined


Correct Answer :

9 years


Explanation :

Total age of 5 members, 10 years ago = (25 * 5) years = 125 years

Total age of 5 members now = (125 + 10 * 5) years = 175 years

Total age of 7 members now = (27 * 7) years = 189 years

Sum of the ages of 2 children = (189 - 175) years = 14 years

Let the age of the younger child be x years.

Then, age of the elder child = (x + 4) years

So, x + x + 4 = 14 <=> 2x = 10 <=> x=5

Hence, Age of younger child = 5 years,
And age of the elder child = (x + 4) years=>(5 + 4) years=>9 years

Three years ago the average age of a family of 5 members was 27 years. On the addition of a child to the family, the present average age of the family is still 27 years. Find the present age of the child?

A)
16 years

B)
12 years

C)
24 years

D)
20 years


Correct Answer :

12 years


Explanation :

sum of 5 members ages 3 years ago = 5 * 27 = 135
in present sum of 5 members ages = 135 + 5*3 = 150

let age of child is x
Sum of 6 members ages now:
150 + x = 6 * 27
150 + x = 162
age of child x = 12

The total ages of Ruhi, Richa and Reema is 60 years. What was the total of their ages 3 years ago?

A)
57years

B)
52 years

C)
51 years

D)
54 years


Correct Answer :

51 years


Explanation :

let the present ages of Ruhi, Richa and Reema are X ,Y and Z
and as per question X+Y+Z=60 years

then 3 years ago total ages of them is X-3+Y-3+Z-3=(X+Y+Z)-9=60-9=51 years

The average age of 5 members of a family is 21 years. If the age of the youngest member be 5 years,find the average age of the family at the time of the birth of the youngest member?

A)
24 years

B)
25 years

C)
20 years

D)
28 years


Correct Answer :

20 years


Explanation :

At present the total age of the family = 5 * 21 = 105
The age of the youngest member be 5 years
The total age of the remaing family member during 5 year 4*5=20 after birth of youngest member


The total age of the family at the time of the birth of the youngest member that is 5 year ago => present the total age of the family -age of the youngest member- change in total age of the remaing family member during 5 year
=> 105-5-20 = 80

Therefore, average age of the family at the time of birth of the youngest member =>total age of the family at the time of the birth of the youngest member / number of member in family at the time of birth of the youngest member
=>80/4 = 20

The ratio of the ages of a father and his son 10 years hence will be 5 : 3, while 10 years ago, it was 3 : 1. The ratio of the age of the son to that of the father today, is?

A)
1:2

B)
1:3

C)
2:3

D)
2:5


Correct Answer :

1:2


Explanation :

Let , the present age of father is f and age of son is s
10 years ago ratio of their ages, (f-10)/(s-10)=3/1
f-10=3s-30=>f-3s=-20
f=3s-20

10 years after ratio of their ages, (f+10)/(s+10)=5/3
3f+30=5s+50
3f-5s=20
substitute value of f here
3(3s-20)-5s=20
9s-60-5s=20
4s=80
s=20

if s=20 then f=3s-20=60-20=40
Hence f = 40, s = 20, ratio of son to father age is s/f=20/40 =1/2

Mr. Ajay is 4 times as old as his son. Four years later the sum of their ages will be 43 years. The present age of son is ?

A)
5 years

B)
7 years

C)
8 years

D)
10 years


Correct Answer :

7 years


Explanation :

Let the son's present age be x years then , (x + 4) + (4x + 4) = 43
5x = 35
Thus, x = 7

The respective ages of father and his son are 41 and 16 years. In how many years will the father be twice as old as his son ?

A)
19 years

B)
9 years

C)
10 years

D)
15 years


Correct Answer :

9 years


Explanation :

Suppose x years later the father will be twice as old as his son.
Then, x + 41 = 2 (x + 16)
⇒ x = 41 - 32 = 9 years

The difference between the ages of Meena and Seema is 3 yr and the ratio between their ages is 7 : 8. What is the sum of their ages ?

A)
43 yr

B)
41 yr

C)
45 yr

D)
48 yr


Correct Answer :

45 yr


Explanation :

Let the present of Meena and Seema are 7k yr and 8k yr, respectively.
Then, 8k - 7k = 3
k = 3

Hence, required sum = 8k + 7k = 15k = 15 * 3 => 45 yr

Ajay is 15 years elder than Rohan. If 5 years ago, Ajay was 3 times as old as Rohan, then find Ajay's present age.

A)
32.5 years

B)
27.5 years

C)
25 years

D)
24.9 years


Correct Answer :

27.5 years


Explanation :

Let age of Rohan be y
Ajay is 15 years elder than Rohan,So Ajay’s age = (y + 15).
5 years ago, Ajay is 3 times as old as Rohan
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25
y = 12.5
Rohan's age = 12.5 years
Ajay's age = (y + 15) = (12.5 + 15) = 27.5 years

One year ago, ratio of Harry and Ram age's was 5 : 6 respectively. After 4 years, this ratio becomes 6 : 7. How old is Ram?

A)
24 years

B)
31 years

C)
25 years

D)
26 years


Correct Answer :

31 years


Explanation :

Let one year ago, Harry’s age = 5x and Ram's age = 6x
Hence at present, Harry’s age = 5x +1 and Ram’s age = 6x +1
After 4 years, this ratio becomes 6 : 7.
Therefore, Harry’s Age / 6 = Peter’s Age / 7
=>((5x +1) + 4) / ((6x +1) + 4) = 6 / 7
7 (5x + 5) = 6 (6x + 5)
35 x + 35 = 36x + 30
36x – 35x = 35 – 30
x = 5
Ram’s present age = (6x + 1)
= (6 * 5) + 1
= 31 years

Raju age after 15 years will be 5 times his age 5 years back, What is the present age of Raju ?

A)
24

B)
10

C)
25

D)
26


Correct Answer :

10


Explanation :

Let the present age of Raju is x,then after 15 years
x+15 = 5(x-5)
x + 15 = 5x – 25
5x – x = 25 + 15
4x = 40
x = 40 / 4
x = 10

Sachin is younger than Ajay by 7 years. If the ratio of their ages is 7:9, find the age of Sachin ?

A)
24

B)
23.5

C)
25

D)
24.5


Correct Answer :

24.5


Explanation :

Let Ajay age is x, then Sachin age is x-7,
So, Sachin’s Age / Ajay ’s Age => (x-7)/x = 7/9
9(x – 7) = 7x
9x-63 = 7x
9x – 7x = 63
2x = 63
x = 31.5
So Sachin age is, x-7 => 31.5 - 7 = 24.5

The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years ?

A)
7:8

B)
3:8

C)
7:9

D)
5:8


Correct Answer :

7:8


Explanation :

Let P age and Q age is 6x years and 7x years.
As given, 7x - 6x = 4
x = 4
So required ratio will be (6x+4)/ (7x+4)
=> 28 / 32
=> 7/8

The present ages of Madhu and Puja is in the ratio 2 : 6. After 5 years, the ratio of their ages will be 3 : 4. What is the average of their ages after 10 years from now?

A)
11 years

B)
12 years

C)
13 years

D)
14 years


Correct Answer :

12 years


Explanation :

Let,the present age Madhu is 2x and Puja is 6x
After 5 years,the ratio of their ages, (2x+5)/(6x+5)=3/4
8x+20=18x+15
10x=5
x=1/2
So,the present age Madhu is 1 year and Puja is 3 year
The average of their ages after 10 years is {(1+10)+(3+10)}/2
=24/2
=12

A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is?

A)
12

B)
15

C)
18

D)
20


Correct Answer :

15


Explanation :

Let son’s age be x years. Then, father’s age = (3x) years.
Five years ago, father’s age = (3x – 5) years and son’s age = (x – 5) years.

As given, Five years back, father’s age was four times
So, 3x – 5 = 4 (x – 5)
3x – 5 = 4x – 20
x= 15.

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