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The following question is accompanied by two statements (I) and (II). You have to determine which statement(s) is/are sufficient/necessary to answer the questions. In how many days will A complete the work? I. Ratio of efficiency of A, B and C is 5 : 6 : 9. A takes 8 days more than C to finish the work II. A and B working together can complete the work in 30 days, B is twice efficient than A

The following question is accompanied by two statements (I) and (II). You have to determine which statement(s) is/are sufficient/necessary to answer the questions. In how many days will A complete the work? I. Ratio of efficiency of A, B and C is 5 : 6 : 9. A takes 8 days more than C to finish the work II. A and B working together can complete the work in 30 days, B is twice efficient than A Correct Answer The data in statement I alone or in statement II alone is sufficient to answer the question.

Calculation:

From statement I

Ratio of efficiency of A, B and C is 5 : 6 : 9

A takes 8 days more than C to finish the work

⇒ (9 – 5) units = 8 days

⇒ 4 units = 8 days

⇒ 1 unit = 2 days

∴ A will complete the work in = 5 × 2 = 10 days

From statement II

A and B working together can complete the work in 30 days

⇒ 1/A + 1/B = 1/30

B is twice efficient than A

Ratio of efficiency of A and B is 1x : 2x

⇒ (1x + 2x) units = 30 days

⇒ 3x units = 30 days

⇒ x unit = 10 days

⇒ 1 unit = 10/x days

∴ A will complete the work in = 10/x days

∴ Data in statement I alone or in statement II alone is sufficient to answer the question

Confusion PointsFrom second statement we can find multiple values of  completion days of A, but since the question is of data sufficiency we can say we can find out days so statement 2 alone can answer but answer will depend upon x.

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