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P and Q can complete work in 6 days, Q and R can complete it in 12 days while P and R take 15 days to complete the same piece of work. If P and Q start working, in how many days total work will be completed if R works every fourth day?1. 5 days2. 6.05 days3. 8 days4. 7.5 days |
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Answer» Correct Answer - Option 2 : 6.05 days Given: P and Q can complete work in 6 days. Q and R can complete it in 12 days. P and R took 15 days to complete the same piece of work. R works every fourth day. Concepts used: Efficiency = Work/Time Time = Work/Efficiency Calculation: 1-day work of P and Q = 1/6 1-day work of Q and R = 1/12 1-day work of P and R = 1/15 1 days work of P, Q and R = 1/2[(1/6) + (1/12) + (1/15)] ⇒ 19/120 Work done by P and Q in 3 days = 3/6 = 1/2 Work done by P, Q and R till fourth day = 1/2 + 19/120 = 79/120 Remaining work = 1 – (79/120) = 41/120 Time = Work/Efficiency Time taken by P and Q to complete the remaining work = (41/120)/(1/6) = 2.05 days Total time taken by P, Q and R = 4 + 2.05 days = 6.05 days ∴ P, Q and R complete the work together when P and Q are assisted R on every fourth day in 6.05 days. |
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