Time & Work · Set 1

Read the formula sheet first, then work through the 15 questions below. Each answer comes with a step-by-step solution — read it even when you get the question right, the shortcut is often faster than your method.

Formula sheet

• If A does a work in n days, A’s 1 day work = 1/n. Together (A+B) 1-day work = 1/a + 1/b ⇒ time = ab/(a+b).
• Work = Rate × Time. Total work = LCM of days (pick units).
• If A is k times as efficient as B, A takes 1/k of B’s time. Efficiency ∝ 1/time.
• Men–days: M₁D₁H₁ / W₁ = M₂D₂H₂ / W₂.
• Pay is shared in the ratio of work done (efficiency × days).
• Alternate-day work: compute the 2-day cycle work first.
• If A and B together take x days, and A alone takes a, then B alone = ax/(a−x).

Practice

Pick an answer to see whether it is right and the worked solution. Your score is saved when you finish the set.