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ATQ,
Let the total work be the LCM of [10, 15, 20] = 60 units. Efficiency of ‘P’ = 60/10 = 6 units/day. Efficiency of ‘Q’ = 60/15 = 4 units/day. Efficiency of ‘R’ = 60/20 = 3 units/day. Work done on the first day = 6 × 1 = 6 units. Work done on the second day = (6 + 4) × 1 = 10 units. Work done on the third day = (6 + 3) × 1 = 9 units. Total work done in the first three days = 6 + 10 + 9 = 25 units. Remaining work = 60 – 25 = 35 units. Time taken to complete the remaining work = (6/6) + (10/10) + (9/9) + (10/17) ≈ 3 + (10/17) ≈ 3.59 days. Total time = 3 + 3.59 = 6.59 days.
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