Problems On Ages - Aptitude MCQ Questions and Solutions with Explanations

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.

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

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{mother's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}{\text{.}} \cr & {\text{Then,}}\,{\text{the}}\,{\text{person's}}\,{\text{present}}\,{\text{age}} \cr & = {\frac{2}{5}x} \,\,{\text{years}} \cr & \therefore {\frac{2}{5}x + 8} = \frac{1}{2}\left( {x + 8} \right) \cr & \Rightarrow 2\left( {2x + 40} \right) = 5\left( {x + 8} \right) \cr & \Rightarrow x = 40 \cr} $$

Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question: R - Q = ?.
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined.

Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20
∴ Required ratio
= (3x + 10) : (x + 10)
= 70 : 30
= 7 : 3

Let Nishi's age be 6x years,
Then Vinnee's age = 5x years
$$\eqalign{ & \therefore \frac{{6x + 9}}{{5x + 9}} = \frac{9}{8} \cr & \Rightarrow 8\left( {6x + 9} \right) = 9\left( {5x + 9} \right) \cr & \Rightarrow 48x - 45x = 81 - 72 \cr & \Rightarrow 3x = 9 \cr & \Rightarrow x = 3 \cr & {\text{Difference in their ages}} \cr & {\text{ = }}\left( {6x - 5x} \right) \cr & = x {\text{ years}} \cr & = {\text{3 years}} \cr} $$

Let Shakti's age be 8$$x$$ years,
Then Kanti's age = 7$$x$$ years
$$\eqalign{ & \therefore \frac{{8x + 10}}{{7x + 10}} = \frac{{13}}{{12}} \cr & \Rightarrow 12\left( {8x + 10} \right) = 13\left( {7x + 10} \right) \cr & \Rightarrow 96x + 120 = 91x + 130 \cr & \Rightarrow 5x = 10 \cr & \Rightarrow x = 2 \cr} $$
Difference between their ages
$$\eqalign{ & = \left( {8x - 7x} \right) \cr & = {\text{ }}x\,{\text{years}} \cr & {\text{ = 2}}\,{\text{years}} \cr} $$

$$\eqalign{ & {\text{A's age = }}\left( {44 \times \frac{6}{{11}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 24 years}} \cr & {\text{And B's age = }}\left( {44 - 24} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 20 years}} \cr} $$
Ratio of their ages after 8 years
$$\eqalign{ & {\text{ = }}\frac{{\left( {24 + 8} \right)}}{{\left( {20 + 8} \right)}} \cr & = \frac{{32}}{{28}} \cr & = \frac{8}{7} \cr & = 8:7 \cr} $$

Let Farah's age 8 years ago be x years.
Then , her present age = (x + 8)
$$\eqalign{ & \therefore x + 8 = \frac{9}{7}x \cr & \Rightarrow 7x + 56 = 9x \cr & \Rightarrow 2x = 56 \cr & \Rightarrow x = 28 \cr} $$
∴ Farah's age now
= (x + 8) years
= (28 + 8) years
= 36
Her daughter's age now
=$$\left( {\frac{1}{6} \times 36} \right)$$   years
= 6 years
Her daughter's age 3 years ago
= (6 - 3) years
= 3 years

Let the daughter's age be x years.
Then, mother age = 3x years
3x + 12 = 2 (x + 12)
⇒ 3x + 12 = 2x + 24
⇒ x = 12
Present age of daughter = 12 years