Problems On Ages - Aptitude MCQ Questions and Solutions with Explanations

Let the son's age be $$x$$ years ,
Then Mr. Sanyal's age = 3$$x$$ years
$$\eqalign{ & \therefore \frac{{3x + 6}}{{x + 6}} = \frac{5}{2} \cr & \Rightarrow 2\left( {3x + 6} \right) = 5\left( {x + 6} \right) \cr & \Rightarrow 6x + 12 = 5x + 30 \cr & \Rightarrow x = 18 \cr} $$
∴ Present age of Mr. Sanyal = 3x years
= (3 × 18) years
= 54 years

Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years,
Then daughter age = (68 - x) years
$$\eqalign{ & \therefore \frac{{x + 4}}{{68 - x + 4}} = \frac{{14}}{5} \cr & \Rightarrow 5\left( {x + 4} \right) = 14\left( {72 - x} \right) \cr & \Rightarrow 5x + 20 = 1008 - 14x \cr & \Rightarrow 19x = 988 \cr & \Rightarrow x = 52 \cr} $$
∴ Daughter's present age
= (68 - 52) years
= 16 years

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Alternate Solution :
According to question,
After 4 years, the total age of man & daughter is
= [(34 × 2) + 4 + 4]
= 76 years
After 4 years their age ratio is 14 : 5 (given)
So, 4 years after the daughter age will be
= 76 × $$\frac{5}{19}$$
= 20 years
∴ Daughter present age
= 20 - 4
= 16 years

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

Let daughter's age be x years.
Suresh's age = 2x years
$$\eqalign{ & \therefore \frac{{2x + 6}}{{x + 6}} = \frac{{23}}{{13}} \cr & \Rightarrow 13\left( {2x + 6} \right) = 23\left( {x + 6} \right) \cr & \Rightarrow 26x + 78 = 23x + 138 \cr & \Rightarrow 3x = 60 \cr & \Rightarrow x = 20 \cr} $$
Present age of Suresh = 2x years
$$\eqalign{ & {\text{ = }}\left( {2 \times 20} \right){\text{ years }} \cr & {\text{ = 40 years}} \cr} $$

Let son's age 10 years ago be x years.
Then, man's age 10 years ago = 7x years
Son's present age = (x + 10) years,
Man's present age = (7x + 10) years
$$\eqalign{ & \therefore {\text{2}}\left[ {\left( {7x + 10} \right) + 2} \right]{\text{ = 5}}\left[ {\left( {x + 10} \right) + 2} \right] \cr & \Rightarrow 2\left( {7x + 12} \right) = 5\left( {x + 12} \right) \cr & \Rightarrow 14x + 24 = 5x + 60 \cr & \Rightarrow 9x = 36 \cr & \Rightarrow x = 4 \cr} $$
Son's present age = (x + 10) years
= (4 + 10) years
= 14 years

Let Samina's age be 7x years.
Then, Suhana's age = 3x years
$$\eqalign{ & \therefore \frac{{7x + 6}}{{3x + 6}} = \frac{5}{3} \cr & \Rightarrow 3\left( {7x + 6} \right) = 5\left( {3x + 6} \right) \cr & \Rightarrow 21x + 18 = 15x + 30 \cr & \Rightarrow 6x + 12 \cr & \Rightarrow x = 2 \cr} $$
Difference in their ages = (7x - 3x) years
= 4x years
= (4 × 2) years
= 8 years

Let A's age be 5x years.
Then, B's age = 6x years
$$\eqalign{ & \therefore \frac{{5x + 6}}{{6x + 6}} = \frac{6}{7} \cr & \Rightarrow 7\left( {5x + 6} \right) = 6\left( {6x + 6} \right) \cr & \Rightarrow 35x + 42 = 36x + 36 \cr & \Rightarrow x = 6 \cr} $$
B's age 5 years ago = (6x - 5) years
= (6 × 6 - 5) years
= 31 years

Let daughter's age be $$x$$ years.
Then, mother's age = (56 $$-\, x\,$$) years
$$\eqalign{ & \left( {56 - x} \right)+4 = 3\left( {x + 4} \right) \cr & \Rightarrow 60 - x = 3x + 12 \cr & \Rightarrow 4x = 48 \cr & \Rightarrow x = 12 \cr} $$
∴ Daughter's age = 12 years
And the mother's age = (56 $$-$$ 12) = 44 years

Let mother's age be 2x years,
Then, son's age = x years
$$\eqalign{ & \therefore \left( {2x - 10} \right) = 3\left( {x - 10} \right) \cr & \Rightarrow 2x - 10 = 3x - 30 \cr & \Rightarrow x = 20 \cr} $$
Son's age = 20 years

$$\eqalign{ & {\text{Ram's father's age}} \cr & {\text{ = 50 years, }} \cr & {\text{Ram's age}} \cr & {\text{ = }}\left( {\frac{3}{5} \times 50} \right){\text{years}} \cr & {\text{ = 30 years}} \cr & {\text{Ram's wife's age}} \cr & {\text{ = }}\left( {\frac{4}{5} \times 30} \right){\text{years}} \cr & {\text{ = 24 years}} \cr & {\text{Ram's son's age}} \cr & {\text{ = }}\left( {\frac{1}{3} \times 24} \right){\text{years}} \cr & {\text{ = 8 years}} \cr} $$