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A and B can do a job together in 7 days. A is 1.75 times as efficient as B. The same job can be done by A alone is :
- a)9.33 days
- b)11 days
- c)12.25 days
- d)16.33 days
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A and B can do a job together in 7 days. A is 1.75 times as efficient ...
Given:
- A and B can do a job together in 7 days.
- A is 1.75 times as efficient as B.
To find:
- The time taken by A to complete the job alone.
Solution:
Let's assume that B takes x days to complete the job alone.
Since A is 1.75 times as efficient as B, it means that A can do 1.75 times the work done by B in the same amount of time.
Therefore, the work done by A in a day = 1.75 * (work done by B in a day)
Calculating the work done by A and B in a day:
- Let's assume the total work to be done is 1 unit.
- B can do 1 unit of work in x days, so the work done by B in a day = 1/x unit.
- A is 1.75 times as efficient as B, so the work done by A in a day = 1.75 * (1/x) = 1.75/x unit.
Calculating the time taken by A and B together:
- The work done by A and B together in a day = (work done by A in a day) + (work done by B in a day)
- = 1.75/x + 1/x = (1.75 + 1)/x = 2.75/x unit
Given that A and B can do the job together in 7 days, it means that the work done by A and B together in a day is equal to 1/7th of the total work.
Therefore, 2.75/x = 1/7
Calculating the value of x:
- Cross-multiplying, we get 2.75 * 7 = x
- x = 19.25
So, B takes 19.25 days to complete the job alone.
Calculating the time taken by A alone:
Since A is 1.75 times as efficient as B, it means that A can do the job in 1.75 times less time than B.
Therefore, the time taken by A alone = 19.25 / 1.75 = 11 days.
Hence, the correct answer is option 'B' - 11 days.
- A and B can do a job together in 7 days.
- A is 1.75 times as efficient as B.
To find:
- The time taken by A to complete the job alone.
Solution:
Let's assume that B takes x days to complete the job alone.
Since A is 1.75 times as efficient as B, it means that A can do 1.75 times the work done by B in the same amount of time.
Therefore, the work done by A in a day = 1.75 * (work done by B in a day)
Calculating the work done by A and B in a day:
- Let's assume the total work to be done is 1 unit.
- B can do 1 unit of work in x days, so the work done by B in a day = 1/x unit.
- A is 1.75 times as efficient as B, so the work done by A in a day = 1.75 * (1/x) = 1.75/x unit.
Calculating the time taken by A and B together:
- The work done by A and B together in a day = (work done by A in a day) + (work done by B in a day)
- = 1.75/x + 1/x = (1.75 + 1)/x = 2.75/x unit
Given that A and B can do the job together in 7 days, it means that the work done by A and B together in a day is equal to 1/7th of the total work.
Therefore, 2.75/x = 1/7
Calculating the value of x:
- Cross-multiplying, we get 2.75 * 7 = x
- x = 19.25
So, B takes 19.25 days to complete the job alone.
Calculating the time taken by A alone:
Since A is 1.75 times as efficient as B, it means that A can do the job in 1.75 times less time than B.
Therefore, the time taken by A alone = 19.25 / 1.75 = 11 days.
Hence, the correct answer is option 'B' - 11 days.
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