120 unit of work can be completed by P alone in 20 days. P started working alone and joined by Q after 10 days such that they completed the remaining work in 6 days. Find the number of days taken by Q to complete the whole work alone.
Let the efficiency of Q = x units/day Efficiency of P = (120/20) = 6 units/day According to question: 6 × 10 + (6 + x) × 6 = 120 Or, 60 + 36 + 6x = 120 Or, 6x = 120 – 96 Or, 6x = 24 Or, x = 4 Number of days taken by Q to complete the work alone = (120/4) = 30 days
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