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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.

36 years

B.

40 years

C.

38 years

D.

36 years

Answer with explanation

Answer: Option BExplanation

Let the mother’s present age be *x* years.

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The ratio of the age of a man and his wife is 4:3. At the time of marriage, the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married?

A.

8 years

B.

12 years

C.

11 years

D.

10 years

Answer with explanation

Answer: Option BExplanation

Let the present age of the man and his wife be 4x and 3x respectively.

After 4 years this ratio will become 9:7

⇒ (4x+4) : (3x+4)= 9:7

⇒ 7(4x+4) = 9(3x+4)

⇒ 28x+28 = 27x+36

⇒ x = 8

The present age of the man = 4x =>> 4×8 = 32

The present age of his wife = 3x =>> 3×8 = 24

Assume that they got married before t years. Then,

⇒ (32−t) : (24−t) = 5:3

⇒ 3(32−t) = 5(24−t)

⇒ 96−3t = 120−5t

⇒ 2t = 24

⇒ t = 24/2 =12

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The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively

A.

30,10

B.

20,20

C.

25,15

D.

20,10

Answer with explanation

Answer: Option AExplanation

Let their ages be x and (x + 20) years.

5 (x – 5) = (x + 20 – 5) or 4x = 40 or x = 10.

Their present ages are 30 years and 10 years

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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.

40

B.

20

C.

30

D.

10

Answer with explanation

Answer: Option CExplanation

Let 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

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

A.

8

B.

4

C.

10

D.

6

Answer with explanation

Answer: Option BExplanation

Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9, x+12.

We know that the sum of their ages is 50.

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

=====>>>>> x= 4

The youngest child is 4 years old.

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

A.

12.5

B.

14.5

C.

24.5

D.

23.5

Answer with explanation

Answer: Option CExplanation

If Rahul age is x, then Sachin age is x-7,

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

=> 9x-63 = 7x

=> 2x = 63

=> x = 31.5

So Sachin age is 31.5 – 7 = 24.5

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The ratio of Rohan’s age 4 years ago and Rahul’s age after 4 years is 1:1. If at present, the ratio of their ages is 5 : 3, then find the ratio between Rohan’s age 4 years hence and Rahul’s age 4 years ago.

A.

4 : 3

B.

1 : 3

C.

3 : 4

D.

3 : 1

Answer with explanation

Answer: Option DExplanation

** **If ages in the numerical are mentioned in ratio A : B, then A : B will be Ax and Bx

1. At present*: *Ratio of their ages = 5 : 3. Therefore, 5 : 3 will be 5x and 3x.

=====>>>> Rohan’s age 4 years ago = 5x – 4

=====>>>> Rahul’s age after 4 years = 3x + 4

2. Ratio of Rohan’s age 4 years ago and Rahul’s age after 4 years is 1 : 1

Therefore,

Solving, we get x = 4

3. We are asked to find the ratio between Rohan’s age 4 years hence and Rahul’s age 4 years ago.

Rohan’s age : (5x + 4)

Rahul’s age: (3x – 4)

Ratio of Rahul’s age and Rohan’s age

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