**A can do a piece of work in 24 days A and B can do it in 16 days and A, B and C in 10.2/3 days. In how many days can A and C do it ?**

###### Answers:

A can do a piece of work in = 24 days

(A + B) can do a piece of work in = 16 days

(A + B + C) can do a piece of work in = 10. 2/3 days = 32/3 days

∴ A’s 1 day work = 1/24

(A + B)’s 1 day work = 1/16

(A + B + C)’s 1 day work = 3/32

C’s 1 day work = 3/32 – 1/16

= (3 – 2)/32 = 1/32

(A + C)’s 1 day work = 1/24 + 1/32

= (4 + 3)/96 = 7/96

∴ (A + C) can do the work in = 96/7 days

= 13. 5/7 days