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When they work alone, B needs 25% more time to finish a job than A does. The two finish the job in 13 days in the following manner : A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?
(CAT 2018)
- a)20
- b)16
- c)22
- d)18
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
When they work alone, B needs 25% more time to finish a job than A doe...
Ratio of time taken by A and B to complete the work alone = 1: 1.25 = 4x : 5x
As A complete half of the work alone and B complete 5% of the work alone, so they will complete remaining 45% of work in 4 days .
So time taken by them to complete the whole work together = 4 * 100/45 = 80/9
Or (4x*5x)/(4x+5x) = 80/9
x = 4
Thus time taken by B to complete the work alone = 5x = 20 days
Community Answer
When they work alone, B needs 25% more time to finish a job than A doe...
Let's assume that A takes x days to finish the job alone.
Given that B takes 25% more time than A to finish the job alone, B will take (1 + 25/100)x = (5/4)x days to finish the job alone.
We are also given that A and B together finish half of the job in a certain number of days, and B alone finishes the remaining 5% of the job in 5 days.
Let's calculate the time taken by A and B together to finish half of the job:
Since A and B together finish the job in 13 days, they finish half of the job in 13/2 = 6.5 days.
Now, let's calculate the time taken by B to finish the remaining 5% of the job:
Since B finishes the remaining 5% of the job in 5 days, B takes 5/(5/100) = 100 days to finish the entire job alone.
From the given information, we know that A and B together finish half of the job in 6.5 days.
Let's find out how much of the job A finishes in 6.5 days:
Since A finishes the job alone in x days, A finishes (1/x) of the job in 1 day. Therefore, in 6.5 days, A finishes (6.5/x) of the job.
Since A and B together finish half of the job in 6.5 days, A finishes (1/2) of the job in 6.5 days. Therefore, we can write the equation as:
(6.5/x) = (1/2)
Simplifying the equation, we get:
13/x = 1
x = 13
Hence, A takes 13 days to finish the job alone.
Now, let's find out how much of the job B finishes in 6.5 days:
Since B takes (5/4)x days to finish the job alone, B finishes (4/5)x of the job in 1 day. Therefore, in 6.5 days, B finishes (6.5 * 4/5) of the job.
Since A and B together finish half of the job in 6.5 days, B finishes (1/2) - (6.5 * 4/5) = (1/2) - (26/10) = (1 - 26/10)/2 = (10 - 26)/20 = -16/20 = -4/5 of the job.
Since B cannot finish a negative portion of the job, we can conclude that B does not contribute to the job.
Therefore, B alone cannot finish the entire job.
Hence, the correct answer is option A) 20.
Given that B takes 25% more time than A to finish the job alone, B will take (1 + 25/100)x = (5/4)x days to finish the job alone.
We are also given that A and B together finish half of the job in a certain number of days, and B alone finishes the remaining 5% of the job in 5 days.
Let's calculate the time taken by A and B together to finish half of the job:
Since A and B together finish the job in 13 days, they finish half of the job in 13/2 = 6.5 days.
Now, let's calculate the time taken by B to finish the remaining 5% of the job:
Since B finishes the remaining 5% of the job in 5 days, B takes 5/(5/100) = 100 days to finish the entire job alone.
From the given information, we know that A and B together finish half of the job in 6.5 days.
Let's find out how much of the job A finishes in 6.5 days:
Since A finishes the job alone in x days, A finishes (1/x) of the job in 1 day. Therefore, in 6.5 days, A finishes (6.5/x) of the job.
Since A and B together finish half of the job in 6.5 days, A finishes (1/2) of the job in 6.5 days. Therefore, we can write the equation as:
(6.5/x) = (1/2)
Simplifying the equation, we get:
13/x = 1
x = 13
Hence, A takes 13 days to finish the job alone.
Now, let's find out how much of the job B finishes in 6.5 days:
Since B takes (5/4)x days to finish the job alone, B finishes (4/5)x of the job in 1 day. Therefore, in 6.5 days, B finishes (6.5 * 4/5) of the job.
Since A and B together finish half of the job in 6.5 days, B finishes (1/2) - (6.5 * 4/5) = (1/2) - (26/10) = (1 - 26/10)/2 = (10 - 26)/20 = -16/20 = -4/5 of the job.
Since B cannot finish a negative portion of the job, we can conclude that B does not contribute to the job.
Therefore, B alone cannot finish the entire job.
Hence, the correct answer is option A) 20.
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When they work alone, B needs 25% more time to finish a job than A does. The two finish the job in 13 days in the following manner : A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?(CAT 2018)a)20b)16c)22d)18Correct answer is option 'A'. Can you explain this answer?
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