Multiple choice

In the family of Tushar, there are 4 members- Tushar, his wife, his only son and his only daughter. Three years ago, age of Tushar 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. Tushar'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 Tushar 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?

  1. All the three statements together

  2. Only statement III

  3. Only statements II and III together

  4. Only statements I and III together

  5. Only statements I and II together
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let T = Tushar's current age, W = wife's age, S = son's age, D = daughter's age. From statement I: W = T - 7 and W = 2S, so T - 7 = 2S or T = 2S + 7. From statement II: (D+3)/(S+3) = 6/5, so 5(D+3) = 6(S+3) or 5D + 15 = 6S + 18 or 5D = 6S + 3. We need one more equation to solve for four unknowns, but statements I and II give us relationships between T, S, and D. The question asks for daughter's age, and we have D in terms of S from statement II. Statement III gives T+2 = (S+2)+(D+2)-1 which is consistent but not needed. Statements I and II are sufficient.

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