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A works twice as fast as B. if both of them can together finish a work in 12 days, B alone can do it in.
- a)40 days
- b)27 days
- c)36 days
- d)24 days
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A works twice as fast as B. if both of them can together finish a work...
Let time taken by b to do the work=2t
:a= t
1 day work of a and b = 1/2t+1/t=1+2/2t
=3/2t_(1)
1day work of a and b =1/12_(2)
1/12=3/2t
t=18
b can do that work alone =18×2=36
:a= t
1 day work of a and b = 1/2t+1/t=1+2/2t
=3/2t_(1)
1day work of a and b =1/12_(2)
1/12=3/2t
t=18
b can do that work alone =18×2=36
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A works twice as fast as B. if both of them can together finish a work...
Given:
- A works twice as fast as B.
To find:
- How many days B alone can finish the work.
Solution:
Let's assume that B takes x days to finish the work alone.
Ratio of Work:
- Since A works twice as fast as B, the ratio of their work rates is 2:1.
- This means that in the same amount of time, A will complete twice as much work as B.
Work Calculation:
- Let's assume that the total work to be done is 1 unit.
- In 12 days, the combined work of A and B is 1 unit.
- Since A completes twice as much work as B, A completes 2/3 (2 units out of 3 units) of the work in 12 days.
- Similarly, B completes 1/3 (1 unit out of 3 units) of the work in 12 days.
Work Rates:
- A completes 2/3 units of work in 12 days.
- B completes 1/3 units of work in 12 days.
Work Rate Calculation:
- Work rate is calculated as the amount of work done per day.
- A's work rate = (2/3 units) / 12 days = 1/18 units per day.
- B's work rate = (1/3 units) / 12 days = 1/36 units per day.
Time Calculation:
- Time is calculated as the reciprocal of work rate.
- B takes x days to complete 1 unit of work alone.
- Therefore, B's work rate = 1 unit / x days = 1/x units per day.
Equating Work Rates:
Since A's work rate is twice that of B, we can equate the work rates:
1/18 = 2 * (1/x)
1/18 = 2/x
x = 18/2
x = 9
Conclusion:
Therefore, B alone can finish the work in 9 days.
Hence, the correct answer is option C) 36 days.
- A works twice as fast as B.
To find:
- How many days B alone can finish the work.
Solution:
Let's assume that B takes x days to finish the work alone.
Ratio of Work:
- Since A works twice as fast as B, the ratio of their work rates is 2:1.
- This means that in the same amount of time, A will complete twice as much work as B.
Work Calculation:
- Let's assume that the total work to be done is 1 unit.
- In 12 days, the combined work of A and B is 1 unit.
- Since A completes twice as much work as B, A completes 2/3 (2 units out of 3 units) of the work in 12 days.
- Similarly, B completes 1/3 (1 unit out of 3 units) of the work in 12 days.
Work Rates:
- A completes 2/3 units of work in 12 days.
- B completes 1/3 units of work in 12 days.
Work Rate Calculation:
- Work rate is calculated as the amount of work done per day.
- A's work rate = (2/3 units) / 12 days = 1/18 units per day.
- B's work rate = (1/3 units) / 12 days = 1/36 units per day.
Time Calculation:
- Time is calculated as the reciprocal of work rate.
- B takes x days to complete 1 unit of work alone.
- Therefore, B's work rate = 1 unit / x days = 1/x units per day.
Equating Work Rates:
Since A's work rate is twice that of B, we can equate the work rates:
1/18 = 2 * (1/x)
1/18 = 2/x
x = 18/2
x = 9
Conclusion:
Therefore, B alone can finish the work in 9 days.
Hence, the correct answer is option C) 36 days.
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A works twice as fast as B. if both of them can together finish a work in 12 days, B alone can do it in.a)40 days b)27 daysc)36 days d)24 dayse)None of theseCorrect answer is option 'C'. Can you explain this answer?
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