Q can do a work in 15 days and R can do the two-third work done by P and Q together in a day. If R completes the work in 18 days, how many days will it take P to complete the work with R?

Q’s one day work = 1/15 R’s one day work =1/18 Given that R’s one day work = (2 )/3 × (P+Q) ∴ P+Q’s one day work = 1/18 × 3/2 = 1/12 ∴ P’s one day work = 1/12-1/15 = 1/60 Hence, P+R’s one day work = 1/60+1/18 = 13/180 ∴ No. of days taken by P and R to complete the work = 180/13 = `13 11/13` days Alternate Solution: Q R 15 18 LCM = 90 units Eff 6 : 5 R = 2/3(P+Q) 5 = 2/3(P+6) 7.5 = P+6 Hence eff. of P = 1.5 units So P & R together can do this job in =90/(1.5+5) = 90/6.5 = 90/(13/2) = 180/13 days

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