# 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?

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by sanjana1809

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by sanjana1809

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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.

=============================

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.