138 unit of work can be completed by P alone in 23 days. P started working alone and joined by Q after 11 days such that they completed the remaining work in 8 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 = (138/23) = 6 units/day According to question: 6 × 11 + (6 + x) × 8 = 138 Or, 66 + 48 + 8x = 138 Or, 8x = 138 – 114 Or, 8x = 24 Or, x = 3 Number of days taken by Q to complete the work alone = (138/3) = 46 days
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