###### Formulae

1. Age after n years = X + n

2. Age n years ago = X “ n

3. n times the age = nX

4. Age of y = (Ratio of y/Sum of ratios)Ã— sum of ages

5. Age of y = (q/p+q)Ã— A

###### Exercise : Ages MCQ Questions and Answers

**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. |

B. |

C. |

D. |

**Correct Answer : D. 4 years **

**Description :**

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. **
The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?

A. |

B. |

C. |

D. |

**Correct Answer : B. 3:5 **

**Description :**

Let the present ages of the two brothers be x and 2x years respectively.

Then, \( {(x - 5)} \over {(2x - 5)} \) = 1/3

=> 3(x - 5) = (2x - 5)

=> x = 10

Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5

**3. **
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, then how old is B?

A. |

B. |

C. |

D. |

**Correct Answer : C. 10 years **

**Description :**

Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.

∴ (2x + 2) + 2x + x = 27

⇒ 5x = 25

⇒ x = 5.

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

**4. **
Ratio between the Present ages of A & B is 5 : 4. If the age of A, 3 years ago is 2 years more than the age of B 4 years hence then find their total age.

A. |

B. |

C. |

D. |

**Correct Answer : B. 81 years **

**Description :**

Given:

Ratio between the Present ages of A & B is 5 : 4

The age of A, 3 years ago is 2 years more than the age of B 4 years hence

Calculation:

Ratio between the Present ages of A & B is 5 : 4

⇒ Ages of A and B can be represented as 5x and 4x respectively

Now, the age of A, 3 years ago is 2 years more than the age of B 4 years hence

(5x - 3) = (4x + 4) + 2

⇒ x = 9

Total age of A and B = 5x + 4x = 9x

∴ Total age = 9 × 9 = 81 years

**5. **
A year ago, Akash’s father’s age was 9 times that of Akash. After 3 years his father’s age will be 5 times that of his age. How old will Akash be next year?

A. |

B. |

C. |

D. |

**Correct Answer : D. 6 years **

**Description :**

Let one year ago age of Akash’s father be 9x and age of Akash be x.

According to the question

⇒ (9x + 4) / (x + 4) = 5/1

⇒ 9x + 4 = 5x + 20

⇒ x = 4

∴ Age of Akash one year ago = 4 years

Present age of Akash = 4 + 1 = 5 years

∴ Age of Akash next year = 5 + 1 = 6 years

Let the present age of Akash be x.

Let the present age of Akash father be y.

For 1 year ago

⇒ y - 1 = 9(x - 1)

⇒ y = 9x - 8

For after 3 years

⇒ y + 3 = 5(x + 3)

⇒ 9x - 8 + 3 = 5x + 15

⇒ 4x = 20

⇒ x = 5

Age of Akash next year = 5 + 1 = 6 years

∴ The age of Akash next year is 6 years.

**6. **
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. |

B. |

C. |

D. |

**Correct Answer : B. 20 **

**Description :**

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.

**7. **
The present age of A is 11 years more than the Present age of B. After 5 years, The age of A will be 4 times what B was 2 years ago. Find the Present age of A.

A. |

B. |

C. |

D. |

**Correct Answer : C. 19 **

**Description :**

Given:

Present age of A is 11 years more than the Present age of B

After 5 years, The age of A will be 4 times of what B was 2 years ago

Calculation:

Present age A = B + 11

After 5 years,

A + 5 = 4 × (B - 2)

∵ A = B + 11 ,

B + 11 + 5 = 4 × (B - 2)

⇒ B + 16 = (4 × B) - 8

⇒ 3 × B = 24

∴ B = 8

⇒ A's present age = B + 11 = 8 + 11 = 19 years

**8. **
The average age of a mother and her son is 45 yrs. The ratio of their ages is 3 : 2. Find the age of the son.

A. |

B. |

C. |

D. |

**Correct Answer : C. 36 years **

**Description :**

Given:

The average age of Mother and son = 45 yr

Mother and son’s age ratio = 3 : 2

Calculations:

Let the age of Mother be 3x.

Let the age of the son be 2x.

According to the question

⇒ \( {(3x + 2x)} \over 2 \) = 45

⇒ 5x = 90

⇒ x = 18

Son’s age = 2 × 18 = 36 yrs.

∴ Son’s age is 36 years.

As the average of the ages = 45 years

⇒ Sum of their ages = 45 × 2 = 90 years

⇒ Age of the son = \( 2 \over 5 \) × 90 = 36 years

**9. **
Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?

A. |

B. |

C. |

D. |

**Correct Answer : A. 35 years **

**Description :**

Let the present ages of X and Y be 5x and 6x years respectively.

Then, (5x + 7)/(6x + 7) = 6/7

7(5x + 7) = 6(6x + 7) => x = 7

X's present age = 5x = 35 years.

**10. **
Six years ago, the ratio of 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. |

B. |

C. |

D. |

**Correct Answer : B. 16 years **

**Description :**

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

Then, [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10

10(6x + 10) = 11(5x + 10) => x = 2

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