Multiple choice

How many days A, B and C can complete the work together? Statement I – Ratio of efficiency of A and B is 2:1. B and C can complete the work in 12 days. Statement II – Ratio of efficiency of A and C is 3:1. C can alone complete the work in 30 days.

  1. Only Statement I alone

  2. Only Statement II alone.

  3. Both Statements I and II together.

  4. Neither Statement I nor II is sufficient.

  5. Either Statement I or II.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the ratio of A:B and the combined rate of B+C. Statement II gives the ratio of A:C and the rate of C. Together, these provide enough information to determine the individual efficiencies of A, B, and C, allowing the calculation of their combined work time.

AI explanation

Statement I provides the efficiency ratio of A and B but gives no information about C's individual capacity, so it is insufficient alone. Statement II gives the efficiency ratio of A and C and states that C alone takes 30 days, but it lacks the connection to B's capacity, making it insufficient alone. When combined, you can deduce the efficiency ratio of A, B, and C as 6:3:1, allowing you to find their combined daily work and determine the total days taken by all three together. Therefore, both statements together are required to answer the question.

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