Multiple choice

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

  1. 10:11

  2. 11:10

  3. 20:21

  4. 21:20
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C Correct answer
Explanation

Q's rate: 1 task / (25 * 12) = 1/300 per hour. R's rate: 1 task / (50 * 12) = 1/600 per hour. Q worked 5 days * 12 hours = 60 hours. Work Q = 60/300 = 1/5. R worked 7 days * 18 hours = 126 hours. Work R = 126/600 = 21/100. Ratio Q:R = 1/5 : 21/100 = 20/100 : 21/100 = 20:21.

AI explanation

Since Q and R are working on the same project, their work done is directly proportional to the product of their efficiencies and their total working hours. Q takes sick leave for the first 2 days, leaving 5 days of work at 12 hours a day, so Q works for 60 hours. R works every day for the 7 days at 18 hours a day, totaling 126 hours. Because their base rates are inversely proportional to their given solo completion periods of 25 and 50 days, the ratio of their work is (60 multiplied by 1/25) to (126 multiplied by 1/50), which simplifies to 12/5 divided by 63/25, resulting in a ratio of 20:21.

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