P, Q, R can do a piece of work in 40 days, 90 days, and 36 days, respectively. P started the work. Q joined him after 8 days. If R joined them after 9 days from the beginning, then for how many days did R work?
LCM (40, 90, 36) = 360 Let the total work be the LCM of the time taken individually by the workers. Efficiencies, P does each day = 360 /40 = 9 units Q does each day = 360/ 90 = 4 units R does each day = 360 /36 = 10 units Let the total work be completed in K days. According to the question, 9 x K + 4 x (K-8) + 10 x (K - 9) = 360 9K+4K-32+10K-90=360 23K= 482 K = 482/23 (K-9) = (482/23) -9 = (482-207)/23=275/23 (K - 9) = 11(22/23) days.
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