**Aptitude questions and answers on numbers and ages**

1. 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. 4 years

B. 8 years

C. 10 years

D. None of these

**Explanation:**

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

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

5x = 20

x = 4.

Age of the youngest child = x = 4 years.

2. Father is four times more than the age of his daughter. If after 5 years, he would be four times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?

A. 1.5 time

B. 2 times

C. 2.5 times

D. 3 times

**Explanation:**

Let the daughter's age be y and father's age be 4y.

Father’s age is 4 times more aged than his daughter, therefore father’s present age = y + 4y = 5y

After five years, the father’s age will be three times his daughter's age.

(4y + 5) = 3 (y + 5)

y = 10

After 5 years it was (4y + 5), then after further 5 years, father’s age = (4y +10) and daughter’s age = (y + 10)

(4y + 10) / (y + 10) = ?

Substituting the value of y, we get

[(4x10) + 10] / [10+10] = 5/2 = 2.5

After another 5 years, the father will be 2.5 times of daughter's age.

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

A. 15

B. 14

C. 10

D. 8

**Explanation:**

Clearly,

x+15 = 5(x-5)

<=> 4x = 40 => x = 10

4. What is John’s present age, if after 10 years his age will be 5 times his age 5 years back.

A. 6.2 years

B. 7.7 years

C. 8.7 years

D. 10 years

**Explanation:**

1) Let John’s present age be x

2) John’s age before 5 years = (x - 5)

3) John’s age after 10 years = (x + 10)

We are given that, John’s age after 10 years (x + 10) is 5 times his age 5 years back (x – 5)

Therefore,

(x + 10) = 5 (x – 5)

Solving the equation, we get

x + 10 = 5x – 25

4x = 35

x = 8.75 years

5. Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?

A. 45

B. 40

C. 35

D. 30

**Explanation:**

Let the present age of P and Q be 3x and 4x respectively.

Ten years ago, P was half of Q's age

(3x-10)=1/2(4x-10)?6x-20=4x-10=> 2x=10=>x=5

Total of their present ages=3x+4x=7x=7×5=35

6. When Rajesh was born, his father age was 29 years older than his brother and his mother was 25 years older than his Sister. If his brother is 2 years elder than his Sister. After 6 years the average age of the family is 20. Then what is the age of Mother when Rajesh was born?

A. 27

B. 28

C. 29

D. 30

**Explanation:**

Sister = x; Brother = x+2; Father = 29+x+2; Mother = 25+x

Present age – 4x+58

After 6 years

4x+58+30 = 4x+88

4x+88 = 100

x = 3

Mothers age = 25+x = 28.

7. Mindy’s current age is 3 times that of her daughter, Cindy. 4 years ago, Mindy’s age was 4 times that of her daughter, what will be Cindy’s age 5 years from now?

A. 17 Years

B. 21 Years

C. 27 Years

D. 15 Years

**Explanation:**

Let Cindy’s current age be x. Then Mindy’s age is 3x.

According to the question,

3x-4=4(x-4)

Or, 3x-4=4x-16

Or, x=12.

Thus, 5 years from now, Cindy’s age will be 12+5=17years.

8. The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?

A. 30

B. 25

C. 20

D. 15

**Explanation:**

Let's take the present age of the elder person = x and the present age of the younger person = x 16 (x 6) = 3 (x-16-6) => x 6 = 3x 66 => 2x = 60 => x = 60/2 = 30

9. 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. None of these

**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.

10. The sum of the present ages of Ashok, Anil, and Ajay is 75 years.If 5 years ago the ratio of their ages was 3: 4: 5, What is the present age of Anil?

A. 26 Years

B. 25 Years

C. 32 Years

D. 65 Years

**Explanation:**

Let 5 years ago, the age of Ashok, Anil, and Ajay were 3x, 4x, and 5x years. Then, their present ages are ( 3x + 5), (4x + 5) and ( 5x + 5) years.

Now, 3x +5 + 4x +5 + 5x + 5 = 75 => 12x = 60 x = 5

Hence, present age of Anil = 4x + 5 = 4 x 5 + 5 = 25 years.

11. Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin?

A. 16 years

B. 18 years

C. 28 years

D. Cannot be determined

E. None of these

**Explanation:**

Let Rahul's age be x years. Then, Sachin's age = (x-7) years.

x-7 / x = 7 / 9 <=> 9x - 63 = 7x <=> 2x = 63 <=> x = 31.5.

Hence, Sachin's age = ( x - 7 ) = 24.5 years.

12. A father said to his son, " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was :

A. 14

B. 19

C. 33

D. 38

**Explanation:**

Let the son's present age be x years .Then, (38 - x) = x => x= 19.

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

13. Ten years ago A was half of B in age. If the ratio of their present ages is 3: 4, what will be the total of their present ages?

A. 30

B. 35

C. 37

D. 41

**Explanation:**

Let A's age 10 years ago = x years.

Then, B's age 10 years ago = 2x years.

(x + 10) / (2x+ lO) = 3/4

=> x = 5.

So, the total of their present ages =(x + 10 + 2x + 10)

= (3x + 20) = 35 years.

14. My present age is 432 times the reciprocal of my age 6 years back. What is my present age?

A. 24 years

B. 25 years

C. 23 years

D. 26 years

**Explanation:**

Let the present age be x. Then x=432/x-6. At this stage, a better option is that you try putting the given answers into this expression one by one. The other option is to simplify this expression into a quadratic equation x×(x-6) = 432. This can now be solved to give x = 24 years.

15. Ten years ago, the age of the mother was three times the age of her son. After ten years, the mother’s age will be twice that of his son. Find the ratio of their present ages.

A. 11: 7

B. 9: 5

C. 7: 4

D. 7 : 3

**Explanation:**

10 years ago, the age of the mother was three times the age of her son. Say, the age of son was x, and mother's age was 3x.

At present: Mother's age is (3x + 10) and son’s age is (x + 10)

After ten years: Mother's age will be (3x + 10) +10 and son’s age will be (x + 10) + 10. Given that, the mother’s age is twice that of the son after ten years.

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

(3x + 20) = 2[x + 20]

Solving the equation, we get x = 20

(3x + 10): (x + 10) = 70: 30 = 7: 3.

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