With P starting the work, working on alternate days, P and Q can finish a work in 17 days. If Q works on the first day and Q and P work alternately, the work is finished in 53/3 days. How many days will each take individually to execute the work?

Explanation

ˆLet P's 1 day work = x and Q's 1 day work = y If P start the work, working on alternate days, P and Q can finish a work in 17 days. P works for = 9 days Q works for = 8 days Total work = 9x + 8y If Q works on the first day and P and Q work alternately, the work is finished in 53/3 days =53/3 = 17+(2/3) Days Q works for = 9 days P work for = 8 + (2/3) = 26/3 days Total work = 9y + 26x/3 According to the question 9x + 8y = 9y + 26x/3 9x-26x/3 = 9y-8y x/3 = y x: y =3:1 Total work = 9x + 8y = 9×3+8×1 = 35 Q alone can finish the whole work in = 35/1 = 35 P alone can finish the whole work in = 35/3 days.