Question
Each question below is followed by two statements I and
II. You have to decide whether the data given in the statements are sufficient to answer the question. What is the present age of Rahul? I. Rahul is 4 years older than twice the present age of his sister. The sum of their present ages is 34 years. II. Four years ago, the ratio of Rahul’s age to his sister’s age was 9 : 5.Solution
ATQ, From I: Let Rahul’s age = R, sister’s age = S. R = 2S + 4 R + S = 34 Substitute R: (2S + 4) + S = 34 3S = 30 ⇒ S = 10, R = 24 Unique value for R ⇒ I alone is sufficient. From II: (R − 4) : (S − 4) = 9 : 5 ⇒ (R − 4)/(S − 4) = 9/5 ⇒ 5R − 20 = 9S − 36 ⇒ 5R − 9S = −16 Only one equation in two unknowns ⇒ infinitely many positive solutions. II alone is not sufficient.
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