Question

A alone can do a work in 8 days. A and B can do it in 6 days . If B has to work alone. how many days the work will get completed

Answer 1

A alone can do a piece of work = 8 days
Amount of work A can do in 1 day =1/8
A and B can do the work = 6 days
Amount of work A and B can do in 1 day = 1/6

A.T.Q
1/6 - 1/8 = [Work done by B in 1 day]
LCM of 6 and 8 = 24
1/6 = 8/24 (Amount of work A and B can do in 1 day)
1/8 = 6/24 (Amount of work A can do in 1 day)

Now, 8/24 - 6/24
=2/24
=1/14
So, B is going to complete 1/14 piece of work in 1 day and will complete the whole work all alone in 14 days.

ANSWER 14 DAYS

Answer 2

let work to be done=w
for A ---- rate(a)*8=w-------------eq1
for B ---- rate(b)*x=w     ----------eq2
for A+B----rate(a)*6+rate(b)*6=w--------eq3
rate(a)=w/8   :::>from eq 2 :::>3w/4+r(b)*6=w:::>r(b)=w/(4*6)=w/24
rate (b)=w/24
:::>from eq2 x=24days