Multiple choice

The following questions are accompanied by three statements I, II, and III. You have to determine which statement(s) is/are necessary/sufficient to answer the question? In how many days can the work be done by 9 men and 15 women? I. 6 men and 5 women can complete the work in 6 days. II. 3 men and 4 women can complete the work in 10 days. III. 18 men and 15 women can complete the work in 2 days.

  1. Only I

  2. Only II

  3. Any two

  4. All I, II and III

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let m = 1 man's work/day, w = 1 woman's work/day. From I: 6(6m+5w)=1, so 36m+30w=1. From II: 10(3m+4w)=1, so 30m+40w=1. Solving gives m=1/54, w=1/90. For 9 men and 15 women: daily work = 9/54 + 15/90 = 1/6 + 1/6 = 1/3. Time needed = 3 days. Similarly, II and III together also work (I and III give same equation). Any two statements are sufficient.

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