A and B can do a piece of work in 28 days; B and C can do the same work in 18 days and A, B and C together can do it in 16 days. The time required (in days) to finish the work by A and C is:

Correct option is A

Given:

A & B complete the work in 28 days

B & C complete the work in 18 days

A + B + C complete the work in 16 days

Find the time for A & C together.

Formula Used:

Daily work  = Total work ÷ days 

Solution:

LCM(28, 18, 16) = 1008 units (work)

Daily rates:

A + B = $$\frac{1008}{28} = 36 \, \text{units/day}$$​​

B + C = $$\frac{1008}{18} = 56 \, \text{units/day}$$​​

A + B + C = $$\frac{1008}{16} = 63 \, \text{units/day}$$​​

C's daily work rate:

C = (A + B + C) - (A + B) = 63 - 36 = 27 units/day

A's daily work rate:

A = (A + B + C) - (B + C) = 63 - 56 = 7 units/day

the daily work rate of A & C together:

A + C = 7 + 27 = 34 units/day

Time for A & C = $$\frac{1008}{34} = \frac{504}{17}$$​ =  $$29 \frac{11}{17}$$​  days

Thus, the time required for A & C to finish the work is approximately $$29\frac{11}{17}$$​days.