Can Do Piece Of Work In 10 Days B In 18 Days And B And C Together In 4 Days

A can do a piece of work in 10 days, B in 18 days, and A, B and C together in 4 days. In what time would C alone do it?

Answers:

A can do a piece of work in = 10 days

B can do a piece of work in = 18 days

(A + B + C) can do a piece of work in = 4 days

∴  A’s 1 day work = 1/10

   B’s 1 day work = 1/18

(A + B)’s 1 day work = 1/10 + 1/18 = (9 +5)/90

= 14/90 = 7/45

(A + B + C)’s 1 day work = ¼

∴ C’s 1 day work =1/4  – 7/45

= (45 – 28)/180 = 17/180

∴ C can do the piece of work in = 180/17 days

= 10. 10/17 days