Question

A can do a piece of work in 10 days and b can do it in 12 days. they work together for 3 days. then b leaves and a alone continues. 2 days after that c joins and the work is completed in 2 days more. in how many days can c do it, if he works alone

Answer 1

A can do a work in 10 days
A in 1 day does 1/10 work

B can do the same work in 12 days
B in 1 day can do 1/12 work

Together in 1 day A & B do : (1/10 + 1/12) = 11/60 work
In 3 days they together did 3*11/60 = 11/20 work.
Work remaining = 1 - 11/20 = 9/20 work
A worked alone for 2 more days
A in 2 days did 2*1/10 = 1/5 work.
Work remaining = 9/20 - 1/5 = 9-4/20 = 5/20= 1/4 work

This 1/4 work was completed in 2 days by A and C together.
In 2 days A do 1/5 work
In 2 days: 1/5 + 2*1/c = 1/4
2/c = 1/4 - 1/5 = 1/20 work
In 1 day,1/c = 1/40 work
c= 40 days to complete 1 work.

OR
Take lcm (A,B)---(10,12) = 60..This is total work
So A in 1 day does 6 work && B in 1 day 5 work
Together in 3 days both did 3*(6+5) = 33 work
Work remaining - 60-33 = 27 work
A worked alone for 2 days==12 more work completed
Work remaining = 27-12 = 15 work
This 15 work completed by A & C in 2 days
A in 2 days do 12 work, which means remaining 3 work was done by C in those 2 days.
C in 2 days==3 work
1 day == 1.5 work
x days ==60 work(total work)
x = 60/1.5 = 40 days
Hope this helps