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P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done?
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P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16...
Understanding P's Work Rate
P can complete 2/5 of the work in 10 days. To find P's work rate:
- Total work = 1 (whole work)
- P's work in 10 days = 2/5
- Work done by P in 1 day = (2/5) / 10 = 2/50 = 1/25
Understanding Q's Work Rate
Q can complete 4/5 of the work in 16 days. To find Q's work rate:
- Total work = 1 (whole work)
- Q's work in 16 days = 4/5
- Work done by Q in 1 day = (4/5) / 16 = 4/80 = 1/20
Combined Work Rate
Now, we combine the work rates of P and Q:
- P's work rate = 1/25
- Q's work rate = 1/20
To find their combined work rate, we need a common denominator:
- LCM of 25 and 20 = 100
- P's work rate = 4/100
- Q's work rate = 5/100
Combined work rate:
- Combined rate = (4/100) + (5/100) = 9/100
Time Taken to Complete Work
To find the time taken to complete the whole work when both work together:
- Total work = 1
- Combined work rate = 9/100
Time = Total work / Combined rate = 1 / (9/100) = 100/9 days
Conclusion
P and Q together can finish the work in approximately 11.11 days (or 11 days and 2 hours).
P can complete 2/5 of the work in 10 days. To find P's work rate:
- Total work = 1 (whole work)
- P's work in 10 days = 2/5
- Work done by P in 1 day = (2/5) / 10 = 2/50 = 1/25
Understanding Q's Work Rate
Q can complete 4/5 of the work in 16 days. To find Q's work rate:
- Total work = 1 (whole work)
- Q's work in 16 days = 4/5
- Work done by Q in 1 day = (4/5) / 16 = 4/80 = 1/20
Combined Work Rate
Now, we combine the work rates of P and Q:
- P's work rate = 1/25
- Q's work rate = 1/20
To find their combined work rate, we need a common denominator:
- LCM of 25 and 20 = 100
- P's work rate = 4/100
- Q's work rate = 5/100
Combined work rate:
- Combined rate = (4/100) + (5/100) = 9/100
Time Taken to Complete Work
To find the time taken to complete the whole work when both work together:
- Total work = 1
- Combined work rate = 9/100
Time = Total work / Combined rate = 1 / (9/100) = 100/9 days
Conclusion
P and Q together can finish the work in approximately 11.11 days (or 11 days and 2 hours).
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P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done?
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P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done?.
P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P can do 2/5 of the work in 10 days and Q can do 4/5 of the work in 16 days. If both of them start working together then the time in which the work can be done?.
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