Question

A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed? *

Answer 1

Answer:

12 pm  [ after 6 hours ]

Step-by-step explanation:

A can do 1 piece of work in 4 hours

so in 1 hour he does 1/4 work

B can do 1 piece of work in 12 hours

so in 1 hour he can do 1/12 work

if they do once each alternatively for one hour then total time = 2 hours in one round

work done after A and B do one hour each [ total 2 hours ]  = work done by A in 1 hour + work done by B in 1 hour

= 1/4 + 1/12

=3/12 + 1/12

= 4/12

= 1/3

in 2 hours, 1/3 work is completed

so 1 work is completed in 2 x 3 = 6 hours

so A and B complete the work if they work alternatively for one hour each in 6 hours

starting at 6 am, they complete it at 12 pm