In a family, the combined age of husband, wife and a son is 90 years. The husband is the oldest. The difference in the ages of the husband and wife is rd the age of their son. After 10 years, the age of the son would be half the age of his father. What is the present age of his mother (in years)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 35.
Let the present age of the husband, wife, and son be x, y, and z respectively.
So, x + y + z = 90 .....(1)
Also, z + 10 = (x + 10)/2
⇒ 2z + 20 = x + 10
⇒ x = 2z + 10 .....(2)
The difference in the ages of the husband and wife is rd the age of their son.
So, x - y = z/3
⇒ 2z + 10 - y = z/3 [∵ x = 2z + 10]
⇒ 6z + 30 - 3y = z
⇒ 3y - 5z = 30 .....(3)
Putting the value x = 2z + 10 in equation (1),
2z + 10 + y + z = 90
⇒ y + 3z = 80 .....(4)
From equations (3) and (4), we get
y = 35 and z = 15
Therefore, the present age of the mother is 35 years.