A and B can complete work in 9 days, while B and C can complete the same work in 18 days. When working together A, B and C, can finish the same work in 8 days. How many days will it take for A and C to complete the work together?

Correct option is C

Given:
A and B can complete the work in 9 days.
B and C can complete the same work in 18 days.
A, B, and C together can finish the work in 8 days.
We need to find how many days A and C together will take to complete the work.

Solution:
Let the total work be 144 units (LCM of 9, 18, and 8).
Work done by A and B in 1 day = Total work / Days taken by A and B = 144 / 9 = 16 units/day
Work done by B and C in 1 day = 144 / 18 = 8 units/day
Work done by A, B, and C in 1 day = 144 / 8 = 18 units/day
Work done by A, B, and C in 1 day = Work done by A and B + Work done by C
18 units/day = 16 units/day + C
C = 18 - 16 = 2 units/day
Work done by B and C in 1 day = 8 units/day
8 = B + C
8 = B + 2
B = 8 - 2 = 6 units/day
Work done by A and B in 1 day = 16 units/day
16 = A + B
16 = A + 6
A = 16 - 6 = 10 units/day
Work done by A and C in 1 day = A + C = 10 + 2 = 12 units/day
Total work = 144 units
Number of days = Total work / Work done by A and C in 1 day = 144 / 12 = 12 days
Thus, A and C together can complete the work in 12 days.
Exam Hall Method: ​