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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 along 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?
- a)10:11
- b)11:10
- c)20:21
- d)21:20
Correct answer is option 'C'. Can you explain this answer?
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P,Q,R and S are working on a project. Q can finish the task in 25 days...
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P,Q,R and S are working on a project. Q can finish the task in 25 days...
Q's work efficiency
- Q can finish the task in 25 days working alone for 12 hours a day.
- Q's work efficiency can be calculated as the ratio of the work done by Q to the total work.
- Since Q works for 12 hours a day, the work done by Q in one day is 1/25th of the total work.
R's work efficiency
- R can finish the task in 50 days working alone for 12 hours a day.
- R's work efficiency can be calculated as the ratio of the work done by R to the total work.
- Since R works for 12 hours a day, the work done by R in one day is 1/50th of the total work.
Work done by Q and R after 7 days
- Q worked for 7 days, but took sick leave in the beginning for 2 days. So Q effectively worked for 5 days.
- R worked for 7 days, working 18 hours a day.
- The work done by Q in 5 days is (5 * 12)/25 = 60/25 = 12/5 of the total work.
- The work done by R in 7 days is (7 * 18)/50 = 126/50 = 63/25 of the total work.
Ratio of work done by Q and R
- The ratio of work done by Q and R after 7 days can be calculated by dividing the work done by Q by the work done by R.
- (12/5) / (63/25) = (12/5) * (25/63) = 12/9 = 4/3 = 20/15
Simplifying the ratio to the lowest terms, we get:
- 20/15 = 4/3
Therefore, the ratio of work done by Q and R after 7 days from the start of the project is 4:3, which is option 'C' - 20:21.
- Q can finish the task in 25 days working alone for 12 hours a day.
- Q's work efficiency can be calculated as the ratio of the work done by Q to the total work.
- Since Q works for 12 hours a day, the work done by Q in one day is 1/25th of the total work.
R's work efficiency
- R can finish the task in 50 days working alone for 12 hours a day.
- R's work efficiency can be calculated as the ratio of the work done by R to the total work.
- Since R works for 12 hours a day, the work done by R in one day is 1/50th of the total work.
Work done by Q and R after 7 days
- Q worked for 7 days, but took sick leave in the beginning for 2 days. So Q effectively worked for 5 days.
- R worked for 7 days, working 18 hours a day.
- The work done by Q in 5 days is (5 * 12)/25 = 60/25 = 12/5 of the total work.
- The work done by R in 7 days is (7 * 18)/50 = 126/50 = 63/25 of the total work.
Ratio of work done by Q and R
- The ratio of work done by Q and R after 7 days can be calculated by dividing the work done by Q by the work done by R.
- (12/5) / (63/25) = (12/5) * (25/63) = 12/9 = 4/3 = 20/15
Simplifying the ratio to the lowest terms, we get:
- 20/15 = 4/3
Therefore, the ratio of work done by Q and R after 7 days from the start of the project is 4:3, which is option 'C' - 20:21.
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P,Q,R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hoursa day. R can finish the task in 50 days, working along for 12 hours per day. Q worked 12 hours aday but took sick leave in the beginning for two days. R worked 18 hours a day on all days. Whatis the ratio of work done by Q and R after 7 days from the start of the project?a)10:11b)11:10c)20:21d)21:20Correct answer is option 'C'. Can you explain this answer?
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