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Efficiency of A is 25% more then B and B takes 25 days to complete a piece of work. A started a work alone and then B joined her 5 days before actual completion of the work. For how many days A worked alone?
- a)9
- b)11
- c)10
- d)25
- e)12
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Efficiency of A is 25% more then B and B takes 25 days to complete a p...
Efficiency (A : B) = 5 : 4
Number of days(A : B) = 4x : 5x = 4x : 25
∴ Number of days required by A to finish the work alone = 4x
= 4 x 5 = 20.
A and B work together for last 5 days = 5 x 9 = 45%
Efficiency of A = 5% and B’s efficiency = 4%
∴ No. of days taken by A to complete 55% work = 55/5 = 11days
Number of days(A : B) = 4x : 5x = 4x : 25
∴ Number of days required by A to finish the work alone = 4x
= 4 x 5 = 20.
A and B work together for last 5 days = 5 x 9 = 45%
Efficiency of A = 5% and B’s efficiency = 4%
∴ No. of days taken by A to complete 55% work = 55/5 = 11days
Most Upvoted Answer
Efficiency of A is 25% more then B and B takes 25 days to complete a p...
Efficiency (A : B) = 5 : 4
Number of days(A : B) = 4x : 5x = 4x : 25
∴ Number of days required by A to finish the work alone = 4x
= 4 x 5 = 20.
A and B work together for last 5 days = 5 x 9 = 45%
Efficiency of A = 5% and B’s efficiency = 4%
∴ No. of days taken by A to complete 55% work = 55/5 = 11days
Number of days(A : B) = 4x : 5x = 4x : 25
∴ Number of days required by A to finish the work alone = 4x
= 4 x 5 = 20.
A and B work together for last 5 days = 5 x 9 = 45%
Efficiency of A = 5% and B’s efficiency = 4%
∴ No. of days taken by A to complete 55% work = 55/5 = 11days
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Efficiency of A is 25% more then B and B takes 25 days to complete a p...
Given: Efficiency of A is 25% more than B, B takes 25 days to complete a piece of work, A started alone and B joined 5 days before completion of the work.
Let the efficiency of B be x. Then, the efficiency of A will be 1.25x (25% more than B).
Let the total work be 1 unit.
So, B can complete the work in 25 days. Hence, B's one day work = 1/25.
A's one day work = 1.25x/25 = x/20.
Let A worked alone for 'd' days.
So, A completed d days work = d * (x/20) = dx/20.
When B joined, A and B together completed the remaining work in 5 days.
Total work completed in 5 days by A and B together = 5 * [(x/20) + (1/25)] = 5x/20.
Remaining work to be completed by A and B together = 1 - [dx/20 + 5x/20] = (20 - dx - 5x)/20.
As per the given condition, A and B together completed this remaining work in 5 days.
So, (20 - dx - 5x)/20 * 5 = (20 - dx)/20 * x * 5/4.
Solving this equation we get, dx = 45.
Hence, A worked alone for 9 days (i.e., d = 9).
Therefore, the correct answer is option 'B'.
Let the efficiency of B be x. Then, the efficiency of A will be 1.25x (25% more than B).
Let the total work be 1 unit.
So, B can complete the work in 25 days. Hence, B's one day work = 1/25.
A's one day work = 1.25x/25 = x/20.
Let A worked alone for 'd' days.
So, A completed d days work = d * (x/20) = dx/20.
When B joined, A and B together completed the remaining work in 5 days.
Total work completed in 5 days by A and B together = 5 * [(x/20) + (1/25)] = 5x/20.
Remaining work to be completed by A and B together = 1 - [dx/20 + 5x/20] = (20 - dx - 5x)/20.
As per the given condition, A and B together completed this remaining work in 5 days.
So, (20 - dx - 5x)/20 * 5 = (20 - dx)/20 * x * 5/4.
Solving this equation we get, dx = 45.
Hence, A worked alone for 9 days (i.e., d = 9).
Therefore, the correct answer is option 'B'.
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