In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. Wha

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Q: 142 (IAS/1998)
In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother ?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,12,16,3,6,7,12

keywords: 

{'age': [2, 1, 1, 2], 'daughter': [1, 2, 4, 5], 'father': [15, 3, 10, 14], 'husband': [0, 3, 2, 1], 'couple': [1, 1, 0, 1], 'wife': [2, 3, 2, 2], 'sister': [0, 1, 2, 0], 'years': [1, 0, 0, 2], 'mother': [4, 3, 4, 7], 'half': [5, 2, 5, 2], 'family': [0, 1, 0, 0]}

Let`s solve the problem step by step to determine the age of the mother:

Let`s assume the age of the daughter is x years.

According to the given information:

- The age of the father is three times that of his daughter, so the age of the father is 3x years.

- The age of the son is half of his mother, so the age of the son is (1/2) * (3x - 9) years (since the wife is 9 years younger than her husband).

Given that the brother is seven years older than his sister, we can determine the age of the son:

(1/2) * (3x - 9) = x + 7

3x - 9 = 2x + 14

x = 23

Therefore, the daughter is 23 years old. Now, we can determine the age of the father:

Age of father = 3 * 23 = 69 years

Finally, we can determine the age of the mother:

Age of mother = Age of father - 9 = 69 - 9 = 60 years

Hence, the age of the mother is 60 years.