Problems On Ages - Aptitude MCQ Questions and Solutions with Explanations

31

Rajan got married 8 years ago. His present age is $$\frac{6}{5}$$ times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marrige. The age of Rajan's sister is = ?

A) 32 years B) 36 years C) 38 years D) 40 years

Discuss

Answer & Solution

Answer: Option C

Solution:

Let Rajan's age 8 years ago be x years,
Then, present age = (x + 8) years
$$\eqalign{ & \therefore x + 8 = \frac{6}{5}x \cr & \Rightarrow 5x + 40 = 6x \cr & \Rightarrow x = 40 \cr} $$
Rajan's sister's age 8 years ago
= (40 - 10) years
= 30 years
∴ His sister's age now
= (30+8) years
= 38 years

32

A couple has a son and a daughter. The age of the father is four times that of the son and the age of the daughter is one-third of that of her mother. The wife is 6 years younger to her husband and the sister is 3 years older then her brother. The mother's age is = ?

A) 42 years B) 48 years C) 54 years D) 63 years

Discuss

Answer & Solution

Answer: Option C

Solution:

M → Mother, F → Father, S → Son and D → Daughter
F = 4S, D = $$\frac{1}{3}$$M, M = F - 6 and S = D - 3
$$\eqalign{ & \therefore M = 3D = 3\left( {S + 3} \right) \cr & = 3S + 9 = \frac{3}{4}F + 9 = \frac{3}{4}\left( {M + 6} \right) + 9 \cr & = \frac{3}{4}M + \frac{3}{4} \times 6 + 9 \cr & \Rightarrow \left( {M - \frac{3}{4}M} \right) = \left( {\frac{9}{2} + 9} \right) \cr & \Rightarrow \frac{1}{4}M = \frac{{27}}{2} \cr & \Rightarrow M = \left( {\frac{{27}}{2} \times 4} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 54\,{\text{years}} \cr & \therefore {\text{ The mother is 54 years old}}{\text{.}} \cr} $$

33

Reenu's father was 38 years of age when she was born while her mother was 36 years old when her brother 4 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 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Mother's age when Reenu's brother was born = 36 year
Father's age when Reenu's brother was born = (38 + 4) years = 42 year
Required difference = (42 - 36) years = 6 years

34

A man was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago and you will know how old I am". What is the age of the man ?

A) 18 years B) 20 years C) 24 years D) 32 years

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the present age of the man be x years
Then,
$$\eqalign{ & \Rightarrow {\text{3}}\left( {x + 3} \right) - 3\left( {x - 3} \right) = x \cr & \Rightarrow \left( {3x + 9} \right) - \left( {3x - 9} \right) = x \cr & \Rightarrow x = 18 \cr} $$
∴ The present age of the man is 18 years

35

The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their ages after 6 years will be ?

A) 5 : 2 B) 2 : 1 C) 11 : 7 D) 13 : 9 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the man's age be 7x years ,
Then son's age = 3x years
$$\eqalign{ & \therefore {\text{7}}x \times 3x = 756 \cr & \Rightarrow 21{x^2} = 756 \cr & \Rightarrow {x^2} = 756 \cr & \Rightarrow {x^2} = 36 \cr & \Rightarrow x = 6 \cr} $$
The ratio of their ages after 6 years
$$\eqalign{ & {\text{ = }}\left( {7x + 6} \right):\left( {3x + 6} \right) \cr & = \left( {7 \times 6 + 6} \right):\left( {3 \times 6 + 6} \right) \cr & = 48:24 \cr & = 2:1 \cr} $$

36

The ratio between the parents ages of A and B is 5 : 3 respectively. The ratio between A's age 4 years ago and B's 4 years hence is 1 : 1. What is the ratio between A's age 4 years hence and B's age 4 years ago ?

A) 1 : 3 B) 3 : 1 C) 2 : 1 D) 4 : 1 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let A's age be 5x years, then B's age = 3x years
$$\eqalign{ & \frac{{5x - 4}}{{3x + 4}} = \frac{1}{1} \cr & \Rightarrow 5x - 4 = 3x + 4 \cr & \Rightarrow 2x = 8 \cr & \Rightarrow x = 4 \cr & \therefore \frac{{{\text{A's age 4 years hence}}}}{{{\text{B's age 4 years ago }}}} \cr & = \frac{{5x + 4}}{{3x - 4}} \cr & = \frac{{5 \times 4 + 4}}{{3 \times 4 - 4}} \cr & = \frac{{24}}{8} \cr & = \frac{3}{1} \cr & = 3:1 \cr} $$

37

The ratio between the ages of Neelam and Shiny is 5 : 6 respectively. If the ratio between the one-third age of Neelam and half of Shiny's age is 5 : 9, then what is Shiny's age = ?

A) 25 years B) 30 years C) 36 years D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Let Neelam's age be 5x years and
Shiny's age be 6x years
$$\eqalign{ & \left( {\frac{1}{3} \times 5x} \right):\left( {\frac{1}{2} \times 6x} \right) = 5:9 \cr & \Rightarrow \frac{{5x}}{{3 \times 3x}} = \frac{5}{9} \cr} $$
Thus, Shiny's age cannot be determined

38

18 years ago, a man was three times as old as his son. Now, the man is twice as old as his son. The sum of the present ages of the man and his son is = ?

A) 54 years B) 72 years C) 105 years D) 108 years

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the son's age 18 years ago be x years,
Then man's age 18 years ago = 3x years
$$\eqalign{ & \left( {3x + 18} \right) = 2\left( {x + 18} \right) \cr & \Rightarrow 3x + 18 = 2x + 36 \cr & \Rightarrow x = 18 \cr} $$
Sum of their present ages
$$\eqalign{ & \Rightarrow \left( {3x + 18 + x + 18} \right){\text{years}} \cr & \Rightarrow \left( {4x + 36} \right){\text{years}} \cr & \Rightarrow \left( {4 \times 18 + 36} \right){\text{years}} \cr & \Rightarrow {\text{ 108 years}} \cr} $$

39

The age of a man 10 years ago was thrice the age of his son. 10 years hence, the man's age will be twice the age of his son. The ratio of their present ages is = ?

A) 5 : 2 B) 7 : 3 C) 9 : 2 D) 13 : 4

Discuss

Answer & Solution

Answer: Option B

Solution:

Let son's age 10 years ago be x years,
Then man's age 10 years ago = 3x years
Son's present age = (x + 10) years ,
Man's present age = (3x + 10) years
$$\eqalign{ & \left( {3x + 10} \right) + 10 = 2\left( {x + 10 + 10} \right) \cr & \Rightarrow 3x + 20 = 2\left( {x + 20} \right) \cr & \Rightarrow 3x + 20 = 2x + 40 \cr & \Rightarrow x = 20 \cr} $$
Ratio of present ages of man and the son
$$\eqalign{ & {\text{ = }}\frac{{3x + 10}}{{x + 10}} \cr & = \frac{{3 \times 20 + 10}}{{20 + 10}} \cr & = \frac{{70}}{{30}} \cr & = 7:3 \cr} $$

40

Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. 8 years ago, what was the ratio of Tanya's age to that of her grandfather ?

A) 1 : 2 B) 1 : 5 C) 3 : 8 D) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

16 years ago, let T = x years and G = 8x years
After 8 years from now,
T = (x + 16 + 8) years and G = (8x + 16 + 8) years
$$\eqalign{ & \therefore {\text{8x + 24 = 3}}\left( {x + 24} \right) \cr & \Rightarrow 8x - 3x = 72 - 24 \cr & \Rightarrow 5x = 48 \cr & 8{\text{years ago,}} \cr & {\text{ }}\frac{{\text{T}}}{{\text{G}}} \cr & = \frac{{x + 8}}{{8x + 8}} \cr & = \frac{{\frac{{48}}{5} + 8}}{{8 \times \frac{{48}}{5} + 8}} \cr & = \frac{{48 + 40}}{{384 + 40}} \cr & = \frac{{88}}{{424}} \cr & = \frac{{11}}{{53}} \cr} $$