Multiple choice

Which information is/are sufficient to answer the questions asked? 40 men and 30 women are working together in a field. After working for 5 days, 10 men and 20 women leave the work. How many more days will be required to complete the remaining work? I. 20 men and 15 women together can complete the work in 7.5 days. II. 15 men and 75 women can complete half work in 1.6 days. III. In a day, the work done by four men is equal to the work done by five women.

  1. Any two of the three together are sufficient

  2. II and III only

  3. I or II only

  4. III and II or III

  5. None of these

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A Correct answer
Explanation

Let 1 man's work per day = m, 1 woman's work per day = w. Statement III: 4m = 5w, so m = 5w/4. Statement I: (20m + 15w) × 7.5 = 1 (total work). Substituting: (100w + 15w) × 7.5 = 115w × 7.5 = 862.5w. Total work = (40m + 30w) × 5 + (30m + 10w) × d. Work done in 5 days = 200w + 30w = 230w. Remaining work = 862.5w - 230w = 632.5w. Remaining rate = 30m + 10w = 37.5w + 10w = 47.5w. Days needed = 632.5/47.5 ≈ 13.3 days. Statement II gives consistent total work. Any two of I, II, III together are sufficient.