Question

A and B can do a piece of work in 12 days; A,B and C all working together can do the
same piece of work in 5 days. In how many days can C alone complete the work?

Answer 1

A+B+C= ---------5
A+B = ------------12. LCM of 5&12 is 60 and this will be total work.
now, A+B+C's 1 day work = 60/5=12 unit
A+B's 1 day work = 60/12 = 5 unit
so C's 1 day work = (A+B+C's 1 day work - A+B's 1 day work) = 12-5= 7 unit/day
because total work is 60 unit so time taken by C alone = 60/7days = 8 (4/7) days

Answer 2

Answer:

60/7 days

Step-by-step explanation:

1/A + 1/B + 1C = 1/5 eq1

1/A + 1/B = 1/12 eq2

Eq1 - eq2

1/C = 1/5 -1/12

1/C = (1/60)(12-5)

1/C = 7/60

C = 60/7 days