# A and B together can make a wall in 60 days. A has worked for 12 days, B finishes the remaining work in 36 days. How many days will B take to finish the whole work alone?

1
by sanjana1809

2014-11-24T22:01:43+05:30

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There is an error in the question.  If A and B finish the work in 60 days.  B cannot finish in 36 days after A works for 12 days....  there is some number wrongly given.

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Let A do 1/X of making the wall in a day.  So A can make wall alone in X days.
Let B do 1/Y of making the wall in a day.  So B can make wall alone in Y days.

A+B can do 1/X + 1/Y of wall in a day. Ie.,  (X+Y)/XY amount in a day
So they take,  XY / (X+Y)  number of days.

X Y / (X+Y) = 60    =>    X Y = 60 (X + Y)  = 60 X + 60 Y    ----  equation 1

A worked for 12 days.  So work completed = 12 * 1 / X = 12/X
Remaining work = 1 - 12/X = (X-12)/X
B completes it in 36 days  =>       (X-12) / X  =  36 * 1 / Y

(X - 12) Y = 26 X
XY - 12 Y = 26 X

Substitute value of XY from equation 1,
60 X + 60 Y - 12 Y = 26 X
34 X + 48 Y = 0        =>  X is coming negative...

there is a problem in the question.

In my humble opinion, I think for the first 12 days A and B work together, then A leaves the work which is undertaken by B.
But anyway there is something wrong in the question.