Aptitude : Problems on Ages

(21) The sum of the present ages of Anna, Ben, and Carla is 75 years. If Anna is 10 years older than Ben, and Ben is 5 years older than Carla, how old is Carla?

• (a) 20 years
• (b) 22 years
• (c) 25 years
• (d) 30 years

Answer

Correct Answer: (c) 25 years
Explanation:
Let Carla’s current age be \( C \) years. Ben is 5 years older than Carla, so Ben’s age is \( C + 5 \) years. Anna is 10 years older than Ben, so Anna’s age is \( (C + 5) + 10 = C + 15 \) years.
The sum of their ages is given as \( C + (C + 5) + (C + 15) = 75 \).
Solving for \( C \), we get \( 3C + 20 = 75 \), and thus \( 3C = 55 \).
Solving for \( C \), we find \( C = 25 \) years.

(22) Fifteen years ago, the age of a woman was three times the age of her daughter. If the woman is currently 45 years old, how old is her daughter now?

• (a) 10 years
• (b) 15 years
• (c) 20 years
• (d) 25 years

Answer

Correct Answer: (c) 20 years
Explanation:
Let the daughter’s current age be \( D \) years and the woman’s current age be \( W \) years.
Given that the woman is currently 45 years old, we can write the equation \( W = 45 \).
Fifteen years ago, the woman’s age was \( W – 15 \) years, and the daughter’s age was \( D – 15 \) years.
According to the problem, fifteen years ago, the woman’s age was three times the age of her daughter, so we have \( W – 15 = 3(D – 15) \).
Substituting \( W = 45 \) into the equation, we get \( 45 – 15 = 3(D – 15) \), which simplifies to \( 30 = 3(D – 15) \).
Solving for \( D \), we find \( D = 20 \) years.

(23) A father is three times as old as his son. If the sum of their ages is 48 years, how old is the son?

• (a) 12 years
• (b) 16 years
• (c) 18 years
• (d) 20 years

Answer

Correct Answer: (b) 16 years
Explanation:
Let the son’s current age be \( S \) years and the father’s current age be \( F \) years.
Given that the father is three times as old as his son, we can write the equation \( F = 3S \).
Also, the sum of their ages is given as \( F + S = 48 \).
We can now solve these equations simultaneously. Substituting \( F = 3S \) into \( F + S = 48 \), we get \( 3S + S = 48 \), which simplifies to \( 4S = 48 \).
Solving for \( S \), we find \( S = 16 \) years.

(24) Ten years ago, the age of a mother was five times the age of her son. If the mother’s current age is 45 years, how old is her son now?

• (a) 8 years
• (b) 10 years
• (c) 12 years
• (d) 14 years

Answer

Correct Answer: (b) 10 years
Explanation:
Let the son’s current age be \( S \) years and the mother’s current age be \( M \) years.
Given that the mother is currently 45 years old, we can write the equation \( M = 45 \).
Ten years ago, the mother’s age was \( M – 10 \) years, and the son’s age was \( S – 10 \) years.
According to the problem, ten years ago, the mother’s age was five times the age of her son, so we have \( M – 10 = 5(S – 10) \).
Substituting \( M = 45 \) into the equation, we get \( 45 – 10 = 5(S – 10) \), which simplifies to \( 35 = 5(S – 10) \).
Solving for \( S \), we find \( S = 10 \) years.