Question

time to build wall 50 days.Time to break wall 60 days.How much time to make whole wall if both work A and B alternative day.pls give answer step wise

Answer 1

A's time to build a wall = 50 days
In 1 day A build = 1/50 part of wall

B's time to destroy the wall = 60 days
In 1 day B destroy = 1/60 part of wall

A and B work alternatively:
So in 2 days, the part of wall build=
1/50 - 1/60 = 6-5/300 = 1/300 part [subtraction, because B is destroying what A had built...LCM=300]

In 2 days=====1/300 part completed
In 2*294 days = 294/300 parts completed
Work Remaining =  1 - 294/300 = 6/300 = 1/50 work

Next is A's turn (since a complete cylce is over--AB-AB....)
A in 1 day does 1/50 work
Hence the work is completed in 2*294 + 1 = 589 days

Hope this helps