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When they work alone, B needs 25% more time to finish a job than A does. They 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?
(2018)
  • a)
    16
  • b)
    20
  • c)
    18
  • d)
    22
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
When they work alone, B needs 25% more time to finish a job than A doe...
Let the time taken by A to finish the job be “a” days.
Time taken by B to finish the job = 5a/4 days
Part of the job completed when A and B worked together for 4 days =

Time taken by B alone to complete the entire job = 5a/4 = 20 days.
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Most Upvoted Answer
When they work alone, B needs 25% more time to finish a job than A doe...
Let's assume that A can finish the entire job in x days.

Given that B needs 25% more time than A to finish the job alone, B can finish the job in (x + 25% of x) days, which is equal to (x + 0.25x) days, or 1.25x days.

We are also given that A and B together can finish the job in 13 days.

First, A works alone till half the job is done, which means that A completes 50% of the job in x/2 days.

Then, A and B work together for 4 days, which means that they complete 4/13 of the remaining 50% of the job.

Finally, B works alone to complete the remaining 5% of the job, which means that B completes 5% of the job in (1.25x - x/2 - 4) days.

To find the value of x, we can equate the sum of these three parts to 100% of the job:

x/2 + (4/13) * (100% - 50%) + 5% = 100%

Simplifying this equation, we get:

x/2 + (4/13) * 50% + 5% = 100%

x/2 + (4/13) * 50/100 + 5/100 = 1

x/2 + 2/13 + 1/20 = 1

To simplify the equation further, we can write 2/13 as 20/130 and 1/20 as 13/260:

x/2 + 20/130 + 13/260 = 1

Multiplying through by the least common multiple (LCM) of the denominators, which is 260, we get:

130x + 40 + 13 = 260

130x + 53 = 260

130x = 207

x = 207/130

x = 1.59

Therefore, B alone can finish the entire job in approximately 1.59 * 1.25 = 1.9875 days, which is approximately equal to 2 days.

So, the correct answer is option (B) 20 days.
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When they work alone, B needs 25% more time to finish a job than A does. They 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?(2018)a)16b)20c)18d)22Correct answer is option 'B'. Can you explain this answer?
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