Question

A and B can do a piece of work
independently in 6 days and 4 days
respectively. If they are working on
alternate days starting with A, how long
the work will take to be finished?
​

Answer 1

There are many ways to solve this kind of problem, but I will try to expalin throughly

Lcm of (6,9) = 18 units
A = 18/6 = 3 units in one day
B = 18/9 = 2 units in one day
So when they work together alternatively
In two days = 3+2 = 5 units
In other two day = 3+2 = 5 units
Again in two day = 3+2 = 5 units
Total
In 6 days = 15 units
Remaining = 18 - 15 = 3 units
Now A turn will come to finish this 3 units of work and he will do it in one day only

So total days they took to complete the work = 6+1 = 7 days


Hope it helps