With P starting the work, working on alternate days, P and Q can finish a work in 17 days. If Q works on the first day and Q and P work alternately, the work is finished in 53/3 days. How
many days will each take individually to execute the work?
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A.
P = 35 days; Q = 35 days
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B.
P = 35/3 days; Q = 35 days
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C.
P = 12 days; Q = 35 days
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D.
P = 35 days; Q = 35/3 days
Correct Answer:
B. P = 35/3 days; Q = 35 days
Explanation:
- Context: P and Q work on alternate days. With P starting, the work is finished in 17 days. If Q starts, the work is finished in 53/3 (17.67) days. - Understanding the Cycles: In the first scenario (P starts), P works for 9 days and Q works for 8 days to complete the work. In the second scenario (Q starts), Q works for 9 days and P works for 26/3 days (8.67 days). - Establishing Efficiency: Comparing the two scenarios, the difference in P's work (9 - 8.67 = 0.33 days) is equivalent to the difference in Q's work (9 - 8 = 1 day). This indicates that P is three times as efficient as Q (Efficiency P:Q = 3:1). - Total Work Calculation: Using the first scenario, Total Work = (9 days × 3 units/day) + (8 days × 1 unit/day) = 27 + 8 = 35 units. - Individual Time: P takes 35 units / 3 units/day = 35/3 days. Q takes 35 units / 1 unit/day = 35 days. - Conclusion: P will take 35/3 days and Q will take 35 days to complete the work individually.
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