Multiple choice

Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: Two friends A and B together can complete a piece of work in 10 days. In how many days A alone complete the piece of work? Statement I : B alone can complete half of the work in 12.5 days. Statement II : The efficiency of A is 50% more than that of B.

  1. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. Either Statement I or Statement II alone is sufficient to answer the question.

  4. Neither statement I nor statement II is sufficient to answer the questions.

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B = 1/10. Statement I: B = 1/25, so A = 1/10 - 1/25 = 3/50 (A takes 16.6 days). Statement II: A = 1.5B, so 1.5B + B = 1/10, 2.5B = 1/10, B = 1/25, A = 3/50. Both are sufficient alone.

AI explanation

Statement I alone gives that B completes half the work in 12.5 days, meaning B's full work time is 25 days. Since A and B together take 10 days, A's solo time is calculated as (10 * 25) / (25 - 10) = 16.66 days. Statement II alone provides that A's efficiency is 1.5 times B's, meaning if their combined efficiency is 5 units, A's is 3 and B's is 2; with the 10-day combined time giving 50 total units, A alone takes 50/3 days. Thus, either statement alone provides a unique solution. Either Statement I or Statement II alone is sufficient to answer the question.

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