Question

A and B together can do a piece of work in 36 days. if A alone does the work for the last 10 days, it is completed in 40 days. B alone can do the work in..
Ans.. 45/60/75/90 days... Plz explain this math

Answer 1

A and B can together complete a work in 36 days.
In 1 day A and B does: 1/36 work.
Its said, the work is completed in 40 days, if A works alone for last 10 days.
Means, A and B together worked for 30 days. Then A alone worked to complete the work in 40 days.

A and B in 30 days do: 30* 1/36 = 5/6 work
Work remaining = 1 - 5/6 = 1/6 work
1/6 work done by A in 10 days
1/6== 10 days
1== X
X = 60 days.
A can complete the work alone in 60 days.
In 1 day A does: 1/60 work.
Let in 1 day B does 1/b work
1/36 = 1/60 + 1/b
1/b = 1/36 - 1/60 = 5-3/180 = 2/180 = 1/90
b = 90 days.
Hence B can complete the work alone in 90 days.
Hope it helps.

SHORT CUT
A+B=== 36 days
A completed the work alone in last 10 days and the work was competed in 40 days.
WORK REMAINING:
A+B                         A
6 days                     10 days
L.C.M(6.10) = 30 = Remaining work
A+B effic = 30/6 =5
A's effic = 30/10 = 3
Hence, B's effic = 5-3 = 2 [efficiencies are constant hence doesn't matter whether its determined from total work or remaining work)
TOTAL WORK = TOTAL EFFICIENCY * DAYS
TOTAL WORK = 5*36 = 180
B's time(days) = Work/ffic = 180/2 = 90 days.

Answer 2

Answer:60

Step-by-step explanation: