Multiple choice

Following questions contain two statements as statement I and statement II. You have to determine which statement/s is/are necessary to answer the question and give answer as, A works for 4 days and leaves the job. In how many days can A alone finish the entire work? Statement I: B finishes the remaining work in 8 days. Statement II: A and B together can finish the work in 20/3 days.

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

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question

  4. The data given in both statements I and II together are not sufficient to answer the question

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

Let A's work rate = a, B's work rate = b, and total work = W. From the problem: A works 4 days, completing 4a work, so remaining work = W - 4a. Statement I: B finishes remaining work in 8 days, so 8b = W - 4a. One equation, three unknowns - insufficient alone. Statement II: A and B together finish in 20/3 days, so (a + b) × (20/3) = W. Still two equations, three unknowns - insufficient alone. Combining both statements: From Statement II, W = (20/3)(a + b). Substitute into Statement I: 8b = (20/3)(a + b) - 4a. This gives 8b = (20/3)a + (20/3)b - 4a, or 8b = (20/3 - 12/3)a + (20/3)b = (8/3)a + (20/3)b. Solving gives b = (2/3)a, and substituting back yields a = 1/20 of W per day, so A alone needs 20 days. Both statements together are necessary, making E correct.

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