Multiple choice

Four workers P,Q,R,S complete a work in different days and they individually take 12 days, 36 days , 24 days and 18 days but not in the same order. Their efficiencies are in descending order. If they start work together and after 1 day P left the work and next day Q left the work and next day S left the work, then in how many days R complete the remaining work and what is the ratio of completed work to remaining work after the day S left the work?

  1. 21 days 12 hours & 72:43

  2. 21 days 12 hours & 29:72

  3. 14 days 8 hours & 29:43

  4. 14 days 8 hours & 29:72

  5. None of these

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Workers take 12, 18, 24, 36 days individually. Since efficiencies are descending (most efficient = least days), P=12 days, Q=18 days, R=24 days, S=36 days. Combined work per day = 1/12 + 1/18 + 1/24 + 1/36 = 6/72 + 4/72 + 3/72 + 2/72 = 15/72 = 5/24. Day 1: All work = 5/24, then P leaves. Day 2: Q + R + S work = 1/18 + 1/24 + 1/36 = 4/72 + 3/72 + 2/72 = 9/72 = 1/8 = 3/24, total = 8/24, Q leaves. Day 3: R + S work = 1/24 + 1/36 = 3/72 + 2/72 = 5/72, total = 29/72, S leaves. Remaining work = 1 - 29/72 = 43/72. Ratio completed:remaining = 29:43. R alone does 1/24 per day, so for 43/72 work: (43/72) / (1/24) = (43/72) × 24 = 43/3 = 14 days and 8 hours.