P, Q and R can do some work in 11 days, 20 days and 55 days respectively. In how many days can the work be done, if P gets the assistance of Q and R on alternate days?
Correct Answer:
C. 8
Explanation:
To solve this problem, we first determine the total work by finding the Least Common Multiple (LCM) of the days taken by P, Q, and R. - Total Work = LCM(11, 20, 55) = 220 units.Next, calculate the daily efficiency (work units per day) for each individual: - Efficiency of P = 220 / 11 = 20 units/day
- Efficiency of Q = 220 / 20 = 11 units/day
- Efficiency of R = 220 / 55 = 4 units/dayThe problem states that P works every day and receives help from Q and R on alternate days. This creates a two-day work cycle: - Day 1 (P and Q work): 20 + 11 = 31 units
- Day 2 (P and R work): 20 + 4 = 24 units
- Total work completed in one cycle (2 days) = 31 + 24 = 55 unitsTo find the total time required: - Number of 2-day cycles = Total Work / Work per cycle = 220 / 55 = 4 cycles
- Total Days = 4 cycles × 2 days per cycle = 8 daysThe work will be completed in 8 days.
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