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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?
  • a)
    20
  • b)
    22
  • c)
    16
  • 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 do...
Given Information:
A takes 25% less time than B to complete a job.
A and B together finish the job in 13 days.
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.

Calculations:
Let's assume that A alone takes x days to complete the job. Therefore, B alone will take 1.25x days to complete the job.
Now, according to the given information:
1. A and B together complete the job in 13 days.
2. A completes half of the job alone.
3. A and B work together for 4 days.
4. B completes the remaining 5% of the job alone.
Let's calculate the portion of work done by A and B together in 13 days.
A's work in 13 days = 13/x
B's work in 13 days = 13/(1.25x)
Now, according to the given information:
A completes half of the job in x/2 days.
The work done by A in x/2 days = (x/2)/x = 1/2
Now, A and B work together for 4 days, so the work done by A and B together in 4 days = 4/(1/x + 1/(1.25x))
Now, the remaining 5% of the job is completed by B alone, so the work done by B in 5% of the job = 0.05.

Calculation of B's work:
Now, let's equate the total work done by A and B together to the work done by A alone plus the work done by B alone.
(13/x) = 1/2 + 4/(1/x + 1/(1.25x)) + 0.05
Solving this equation will give us the value of x, which is the number of days B alone takes to complete the entire job.

Final Answer:
After solving the above equation, we get x = 20 days.
Therefore, B alone can finish the entire job in 20 days. Hence, the correct answer is option A.
Free Test
Community Answer
When they work alone, B needs 25% more time to finish a job than A do...
Let us assume that A can complete 'a' units of work in a day and B can complete 'b' units of work in a day.
A works alone till half the work is completed.
A and B work together for 4 days and B works alone to complete the last 5% of the work.
=> A and B in 4 days can complete 45% of the work.
Let us assume the total amount of work to be done to be 100 units.
4a + 4b = 45 --------- (1)
B needs 25% more time than A to finish a job.
=> 1.25*b = a ---------- (2)
Substituting (2) in (1), we get,
5b+4b = 45
9b = 45
b = 5 units/day
B alone can finish the job in 100/5 = 20 days.
Therefore, option A is the right answer.
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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?a) 20b) 22c) 16d) 18Correct answer is option 'A'. Can you explain this answer?
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