In the family of Amit there are 4 members Amit his wife his only son and his only daughter Three yea...........

Quantitative Aptitude (SBI-PO) Data Sufficiency

In the family of Amit, there are 4 members- Amit, his wife, his only son and his only daughter. Three years ago, age of Amit was 4 years more than the sum of the ages of his son and daughter, then what is the present age of their daughter?

I. Amit's wife is 7 years younger to him and her present age is twice the present age of their son.

II. Three years hence, the respective ratio between the ages of his daughter and his son will be 6 : 5.

III. Two years hence, the age of Amit will be 1 years less than the sum of the ages of his son and daughter.

Which of the following statement(s) is/are sufficient to answer the question?

All the three statements together

Only statement III

Only statements II and III together

Only statements I and III together

Only statements I and II together

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Explanation:

Given, (Son’s present age – 3 years) + (Daughter’s present age – 3 years) + 4 years = (Amit's present age – 3 years)
⇒Son’s present age + Daughter’s present age = (Amit's present age – 1 year)
From statement III: (Son’s present age + 2 years) + (Daughter’s present age + 2 years) – 1 year = (Amit's present age + 2 years)
⇒Son’s present age + Daughter’s present age = (Amit's present age – 1 year)
This information is already given in question, so we cannot answer the question from statement III.
⇒
From statement I: Wife's present age = Amit’s present age – 7 years
Wife's present age = 2 × Amit’s son present age
Also, Amit's present age = Wife’s present age + 7 years = 2 × Son’s present age + 7
⇒Son’s present age + Daughter’s present age = (2 × Son's present age + 6 years)
⇒Daughter’s present age = (Son's present age + 6 years)
From statement II: Let 4 years hence the age of Amit’s daughter = 6x years, then
4 years hence the age of Amit’s son = 5x years
3 years ago, the age of Amit = (6x – 4 – 3) + (5x – 4 – 3) + 4 = (11x – 10) years
Present age of Amit = (11x – 10) + 3 = (11x – 7) years
From statements I and II together:
6x – 4 = 5x – 4 + 6
⇒x = 6
Hence, statements I and II together sufficient to answer the question.