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A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time?
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A and B can complete a work in 5 days and 10 days respectively. B star...
Work Rates of A and B
A can complete the work in 5 days, while B can do it in 10 days. Their work rates are:
- A's work rate = 1/5 (work per day)
- B's work rate = 1/10 (work per day)
Work Done by B Alone
B starts the work alone for the first 5 days. In this time, B completes:
- Work done by B in 5 days = 5 * (1/10) = 1/2 of the work
Remaining Work
After 5 days, B has completed half of the work, so:
- Remaining work = 1 - 1/2 = 1/2 of the work
Combined Work Rate of A and B
Once A joins B, their combined work rate is:
- Combined work rate = A's rate + B's rate = 1/5 + 1/10
- To add these fractions, find a common denominator (10):
- 1/5 = 2/10
- So, Combined work rate = 2/10 + 1/10 = 3/10 (work per day)
Time Taken to Complete Remaining Work
To finish the remaining 1/2 of the work with their combined rate of 3/10:
- Time = Remaining work / Combined work rate
- Time = (1/2) / (3/10) = (1/2) * (10/3) = 5/3 days
Total Time to Complete the Work
Adding the initial 5 days B worked alone to the time taken by A and B together:
- Total time = 5 days + 5/3 days
- Convert 5 days to a fraction: 5 = 15/3
Thus,
- Total time = 15/3 + 5/3 = 20/3 days
Final Answer
The total time taken to complete the work is 20/3 days, or approximately 6 days and 2 hours.
A can complete the work in 5 days, while B can do it in 10 days. Their work rates are:
- A's work rate = 1/5 (work per day)
- B's work rate = 1/10 (work per day)
Work Done by B Alone
B starts the work alone for the first 5 days. In this time, B completes:
- Work done by B in 5 days = 5 * (1/10) = 1/2 of the work
Remaining Work
After 5 days, B has completed half of the work, so:
- Remaining work = 1 - 1/2 = 1/2 of the work
Combined Work Rate of A and B
Once A joins B, their combined work rate is:
- Combined work rate = A's rate + B's rate = 1/5 + 1/10
- To add these fractions, find a common denominator (10):
- 1/5 = 2/10
- So, Combined work rate = 2/10 + 1/10 = 3/10 (work per day)
Time Taken to Complete Remaining Work
To finish the remaining 1/2 of the work with their combined rate of 3/10:
- Time = Remaining work / Combined work rate
- Time = (1/2) / (3/10) = (1/2) * (10/3) = 5/3 days
Total Time to Complete the Work
Adding the initial 5 days B worked alone to the time taken by A and B together:
- Total time = 5 days + 5/3 days
- Convert 5 days to a fraction: 5 = 15/3
Thus,
- Total time = 15/3 + 5/3 = 20/3 days
Final Answer
The total time taken to complete the work is 20/3 days, or approximately 6 days and 2 hours.
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A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time?
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A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time?.
A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B can complete a work in 5 days and 10 days respectively. B starts the work and after 5 days A also joins him. In all, the work was finished in what time?.
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