Comparative Efficiency with Time Difference A is thrice as efficient as B. Together they complete the work in 3 days. If B takes 8 days more than A to do the work alone, how many days does A take alone?

Introduction / Context:
This problem couples a relative-efficiency statement (“A is thrice as efficient as B”) with a time difference between their solo durations. Use the inverse relation between efficiency and time to form equations and solve.

Given Data / Assumptions:

• A is 3 times as efficient as B.
• They finish together in 3 days.
• B’s solo time is 8 days more than A’s solo time.

Concept / Approach:
If A is 3 times as efficient as B, then T_A = T_B/3. Also given T_B = T_A + 8. Solve these to find T_A. (The “together in 3 days” statement is a cross-check.)

Step-by-Step Solution:
From efficiencies: T_A = T_B/3.From time difference: T_B = T_A + 8.Substitute: T_A = (T_A + 8)/3 ⇒ 3T_A = T_A + 8 ⇒ 2T_A = 8 ⇒ T_A = 4 days.Check together rate: 1/4 + 1/12 = 1/3 ⇒ 3 days total, consistent.

Verification / Alternative check:
With T_A = 4, T_B = 12 (8 more). The together time is exactly 3 days.

Why Other Options Are Wrong:
2, 6, 12, and 16 days don’t satisfy both the efficiency and the time-difference constraints.

Common Pitfalls:
Confusing “times as efficient” with “times as long”; they are inversely related.

Final Answer:
4