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A and B working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев?
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A and B working separately can do a piece of work in 8 and 10 hours re...
Work Rates of A and B
A can complete the work in 8 hours, which means A's work rate is:
- Rate of A: \( \frac{1}{8} \) of the work per hour
B can complete the work in 10 hours, so B's work rate is:
- Rate of B: \( \frac{1}{10} \) of the work per hour
Combined Work in Two Hours
When A and B work alternately for one hour each, they complete the following in two hours:
- Work done by A in the first hour: \( \frac{1}{8} \)
- Work done by B in the second hour: \( \frac{1}{10} \)
Now, we calculate the total work done in two hours:
- Total work in two hours:
- \( \frac{1}{8} + \frac{1}{10} \)
To add these fractions, find a common denominator (40):
- \( \frac{1}{8} = \frac{5}{40} \)
- \( \frac{1}{10} = \frac{4}{40} \)
Thus,
- Total work done in two hours:
- \( \frac{5}{40} + \frac{4}{40} = \frac{9}{40} \)
Time to Complete the Work
Now, we need to determine how many cycles of two hours it takes to complete the work:
- Work left after each cycle:
- After each 2 hours, \( \frac{9}{40} \) of the work is done.
Let’s find how many such cycles are required to complete the entire work (1 unit):
- Let \( n \) be the number of cycles:
\( n \times \frac{9}{40} = 1 \)
- Solving for \( n \):
\( n = \frac{40}{9} \approx 4.44 \)
This means it takes about 4 full cycles (8 hours), and a bit more work is needed.
Final Adjustment
After 4 cycles (8 hours), A and B have completed:
- \( 4 \times \frac{9}{40} = \frac{36}{40} = \frac{9}{10} \) of the work.
Remaining work:
- \( 1 - \frac{9}{10} = \frac{1}{10} \)
In the next hour (A's turn), A can complete:
- \( \frac{1}{8} \) of the work (which is more than \( \frac{1}{10} \)).
Thus, the total time taken to complete the work is:
- Total time: 9 hours.
A can complete the work in 8 hours, which means A's work rate is:
- Rate of A: \( \frac{1}{8} \) of the work per hour
B can complete the work in 10 hours, so B's work rate is:
- Rate of B: \( \frac{1}{10} \) of the work per hour
Combined Work in Two Hours
When A and B work alternately for one hour each, they complete the following in two hours:
- Work done by A in the first hour: \( \frac{1}{8} \)
- Work done by B in the second hour: \( \frac{1}{10} \)
Now, we calculate the total work done in two hours:
- Total work in two hours:
- \( \frac{1}{8} + \frac{1}{10} \)
To add these fractions, find a common denominator (40):
- \( \frac{1}{8} = \frac{5}{40} \)
- \( \frac{1}{10} = \frac{4}{40} \)
Thus,
- Total work done in two hours:
- \( \frac{5}{40} + \frac{4}{40} = \frac{9}{40} \)
Time to Complete the Work
Now, we need to determine how many cycles of two hours it takes to complete the work:
- Work left after each cycle:
- After each 2 hours, \( \frac{9}{40} \) of the work is done.
Let’s find how many such cycles are required to complete the entire work (1 unit):
- Let \( n \) be the number of cycles:
\( n \times \frac{9}{40} = 1 \)
- Solving for \( n \):
\( n = \frac{40}{9} \approx 4.44 \)
This means it takes about 4 full cycles (8 hours), and a bit more work is needed.
Final Adjustment
After 4 cycles (8 hours), A and B have completed:
- \( 4 \times \frac{9}{40} = \frac{36}{40} = \frac{9}{10} \) of the work.
Remaining work:
- \( 1 - \frac{9}{10} = \frac{1}{10} \)
In the next hour (A's turn), A can complete:
- \( \frac{1}{8} \) of the work (which is more than \( \frac{1}{10} \)).
Thus, the total time taken to complete the work is:
- Total time: 9 hours.
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A and B working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев?
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A and B working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев? 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 working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев?.
A and B working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев? 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 working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately A beginning, in how many hours will the work be completed?селедев?.
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