raghavrf wrote:
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) 16
(C) 22
(D) 18
(E) 24
Since B needs 25% more time to finish a job than A, B will do \(\frac{4}{9}\)th of the work if both A and B work together.
Let the total work be \(x\).
If A finishes half the work to begin with, the work that remains is \(\frac{x}{2}\). Also, B does 5% or \(\frac{x}{20}\) of the work alone.
In 4 days both A and B do \(\frac{x}{2} - \frac{x}{20} = \frac{9x}{20}\) of the work. In 1 day, they will do \(\frac{9x}{80}\) of the work together.
In 1 day, B will do \(\frac{4}{9}*\frac{9x}{80}= \frac{x}{20}\) of the work.
Therefore, B, working alone, can complete the work in
20(Option A) days.
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