Multiple choice

The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. Find the total length of wall built by 2 Men and 3 Women when working together. Statement I: A man takes 20 days to build that wall alone while 1 woman takes 24 days to build the same wall alone. Statement II: A man takes 10 days to build half of that wall alone while 1 woman takes 8 days to build one – third of the same wall alone and length of wall build in 1 day by a man is 6 meters Statement III: Total lengths of wall build in 1 day when all the 5 workers work together is 27 meters.

  1. If the data in statement II alone is sufficient to answer the question

  2. If the data in both statements I and II together is sufficient to answer the question

  3. If the data either in statement I and III is sufficient to answer the question

  4. If the data either in statement II alone or I and III are sufficient to answer the question

  5. Any two of them together are sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: Man builds in 20 days, woman in 24 days. Combined work: 1/20 + 3/24 = 1/20 + 1/8 = 12/240 + 30/240 = 42/240 = 7/40 wall per day. But we don't know wall length. Statement II: Man builds half in 10 days (so full in 20 days, consistent with I). Woman builds 1/3 in 8 days (so full in 24 days, consistent). Also: 1 man-day = 6 meters. So 20 man-days = 120 meters (wall length). 2 men + 3 women in 1 day: 2×6 + 3×(120/24) = 12 + 15 = 27 meters. Statement III: All 5 workers build 27 meters in 1 day. With I & III: We know rates but not length. With II alone: Complete info. With I & III: We have work rates and total output but not individual lengths unless combined with II. Actually, II alone or I & III both work. Option D is correct.

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