In how many days will B alone complete the work? I. A and B together finish in 8 days. II. B and C together finish in 10 days. III. A and C together finish in 12 days.

Introduction / Context:
Given three pairwise times, find B’s solo time.

Concept / Approach:
Let a, b, c be daily rates. Then a + b = 1/8, b + c = 1/10, a + c = 1/12. Solve for b.

Step-by-Step Solution:
Add first two and subtract the third: (a + b) + (b + c) − (a + c) = 1/8 + 1/10 − 1/12.Left side simplifies to 2b ⇒ 2b = 15/120 + 12/120 − 10/120 = 17/120 ⇒ b = 17/240.Therefore B alone finishes in 1/b = 240/17 days.

Why Other Options Are Wrong:
Any two equations leave three unknowns inadequately constrained for a unique b; all three are required.

Final Answer:
I, II and III.