Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? Mark answer - P, Q & R take 25 days to complete a work. How many days will Q take to do it alone ? I. P and Q together take 35 days for the same work. II. P and R together take 35 days for the same work.

  1. statement I alone is sufficient but statement II alone is not sufficient.

  2. statement II alone is sufficient but statement I alone is not sufficient.

  3. each statement alone (either I or II) is sufficient.

  4. statement I and II together are not sufficient.

  5. both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P, Q, R's rates be p, q, r work/day. Given: 1/(p+q+r) = 25, so p+q+r = 1/25. Statement I: 1/(p+q) = 35, so p+q = 1/35. We have p+q+r = 1/25 and p+q = 1/35, giving r = 1/25 - 1/35 = 2/175. But we need q alone, not possible with these two equations (3 unknowns, 2 equations). Statement II: 1/(p+r) = 35, so p+r = 1/35. Now we have p+q+r = 1/25 and p+r = 1/35, giving q = 1/25 - 1/35 = 2/175. So Q alone takes 175/2 = 87.5 days. Statement II alone is sufficient.

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