P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?\nOptions:\n(A) 5 days\n(B) 9 days\n(C) 30 days\n(D) 20 days\n(E) 10 days Stream of consciousness first, then make a decision:
User
Work done by P in 1 day = 1/20\nWork done by Q in 1 day = 1/12\nWork done by P in 4 days = 4 × (1/20) = 1/5\nRemaining work = 1 – 1/5 = 4/5\nWork done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15\nNumber of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6\nTotal days = 4 + 6 = 10
Thus, the answer is (E).
Assistant