A couple has a son and a daughter. The age of the father is four times that of…
2022
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 than her brother. The mother’s age is –
- A.
42 years
- B.
48 years
- C.
54 years
- D.
63 years
Attempted by 20 students.
Show answer & explanation
Correct answer: C
Solution: Use algebra to find the ages.
Let the son’s age be x.
Father’s age = 4x, so mother’s age = 4x − 6 (wife is 6 years younger than husband).
Daughter’s age = x + 3 (sister is 3 years older than brother).
Given that daughter’s age = one-third of mother’s age, set up the equation x + 3 = (4x − 6)/3.
Solve: multiply both sides by 3: 3x + 9 = 4x − 6 ⇒ bring terms together: 9 + 6 = 4x − 3x ⇒ x = 15.
Mother’s age = 4x − 6 = 4×15 − 6 = 60 − 6 = 54 years.
Answer: 54 years.