Multiple choice

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The following table shows the five different projects named X, Y, Z, M and N and four persons working on it. The second table shows the part of respective project that could not be completed by individuals in time. The following table shows the number of days for which 4 individuals A, B, C and D worked on 5 different projects X, Y, Z, M and N. It also shows the part of respective project that could not be completed by individuals in time. Some values are missing which are denoted by symbol (-). With the help of information in questions and table below answer the questions that follow.

Project Z was to be completed in 12 days. To complete project in time, all A, B, C and D decided to work in pairs in alternate days. A and C on 1st day, B and D on 2nd day, A and C on 3rd, and so on. But they could not complete project in time. What percent of project Z remain uncompleted if A, B, C and D can complete whole project Z in 24, 36, 40 and 30 days respectively?

  1. 26.5%

  2. 23.33%

  3. 33.33%

  4. 45.5%

  5. 25%
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B Correct answer
Explanation

Calculate work done by each pair per day. A+C rate = 1/24 + 1/40 = 1/15 per day. B+D rate = 1/36 + 1/30 = 3/35 per day. In 12 days (6 days each pair): A+C do 6×(1/15) = 2/5 = 40%, B+D do 6×(3/35) = 18/35 ≈ 51.43%. Total = 2/5 + 18/35 = 32/35 ≈ 91.43%. Remaining = 1 - 32/35 = 3/35 = 23.33%.

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