Multiple choice

Directions: In the following question, a given questions is followed by information in three statements. You have to decide the data in which statement (s) is sufficient to answer the question and mark your answer accordingly. How many days A, B and C can complete the work together? Statement I - Ratio of efficiency of A and B is 2:1. Band 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: A:B = 2:1, B+C = 12 days. Statement II: A:C = 3:1, C = 30 days. From II, C=30, A=10. From I, B=15. With A, B, and C efficiencies known, we can calculate the time taken to complete the work together.

AI explanation

Statement I alone provides the ratio of A and B as 2:1 and gives the combined time for B and C, but without knowing the individual time of C, it is insufficient. Statement II provides the ratio of A and C as 3:1 and states C alone takes 30 days, which means A takes 10 days, but it lacks information about B. Combining both statements, the efficiencies of A, B, and C are in the ratio 6:3:2, meaning their combined efficiency is 11 units. Since C's efficiency is 2 units and C takes 30 days, the total work is 60 units. Therefore, working together at 11 units per day, they complete the work in 60 divided by 11 days, meaning both statements together are sufficient.

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