Time for A and B together to complete the work — which statements suffice? I. A alone finishes in 8 days. II. If A works 5 days alone and B works 6 days alone, the work is finished. III. B alone finishes in 16 days.

Introduction / Context:We must identify which statements suffice to determine the joint time for A and B working together.

Given Data / Assumptions:

• I: A's time TA = 8 days ⇒ rate a = 1/8 (work/day).
• II: 5 * a + 6 * b = 1 (total work completed by A alone for 5 days and B alone for 6 days).
• III: B's time TB = 16 days ⇒ rate b = 1/16.

Concept / Approach:Joint time T(AB) = 1 / (a + b). Any two statements that allow us to find both a and b will suffice.

Step-by-Step Solution:

Verification / Alternative check:All three pairs yield identical rates a and b, hence the same joint time.

Why Other Options Are Wrong:

• Options listing a single specific pair are too restrictive; multiple pairs suffice.

Common Pitfalls:Adding days instead of rates; forgetting that work equations add linearly in rates.

Final Answer:Any two of the three