Question

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?

Answer 1

Answer:

B alone can finish the job in 16 days

Step-by-step explanation:

Let A finishes the work in x days

A in 1 day does = 1/x work

B finishes the work = x + 0.25x = 1.25x days

B in 1 day does = 1/1.25x work

A does half the work in x/2 days

Reamining job = 50%

B alone does 5% of the job

Therefore, A and B in 4 days did = 45% of work

Thus

$4(\frac{1}{x}+\frac{1}{1.25x})=0.45$

$\implies \frac{1}{x}+\frac{1}{1.25x}=\frac{0.45}{4}$

$\implies \frac{1.25+1}{1.25x}=\frac{0.45}{4}$

$\implies \frac{2.25}{1.25x}=\frac{0.45}{4}$

$\implies \frac{225}{125x}=\frac{45}{400}$

$\implies \frac{9}{5x}=\frac{45}{400}$

$\implies x=\frac{9\times400}{5\times45}$

$\implies x=16$

Therefore, B alone can finish the job in 16 days

Answer 2

Answer:

B alone can finish the entire job in 20 Days

Step-by-step explanation:

Let say A complete the job in  A Days

Then B completes the job  in B Days

B needs 25% more time to finish a job than A

=> B = A + (25/100)A

=> B = 1.25A  

A's 1 day work = 1/A

A works alone till half the job is done  = 1/2

=> Number of Days A worked = A/2

A and B work together for four days

B works alone to complete the remaining 5% of the job

Work done by B alone = (5/100)  = 1/20

Number of Days B worked = B/20  = 1.25A/20   = 0.0625A

A/2 + 4 + 0.0625A = 13

=> A + 0.125A = 18

=> A = 16

B = 1.25A = 16 * 1.25 = 20

B alone can finish the entire job in 20 Days