Discussion
Consider the following statements:
1. If A completes a job in 10 days and B in 15 days, then together they will complete it in 6 days.
2. If 6 workers complete a job in 8 days, then 3 workers will complete it in 16 days (same efficiency).
3. If A is twice as efficient as B, then A takes half the time taken by B to complete the same work.
How many of the statements given above are correct?
Answer: C
All three statements are correct.
Statement 1: \(\tfrac{1}{10} + \tfrac{1}{15} = \tfrac{3 + 2}{30} = \tfrac{1}{6}\), so together they take 6 days.
Statement 2: the job is \(6 \times 8 = 48\) worker-days, so 3 workers need \(48 / 3 = 16\) days.
Statement 3: if A does twice B's work per day, A finishes the same job in half B's time, since time is inversely proportional to efficiency.
Each statement applies the inverse relation between rate and time correctly, so the answer is all three.
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