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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?

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? Correct Answer P = 35/3 days; Q = 35 days

Let P's 1 day work = P and Q's 1 day work = Q

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 = 9P + 8Q

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 = 9Q + 26P/3

According to the question

9P + 8Q = 9Q + 26P/3

⇒ 9P – 26P/3 = 9Q – 8Q

⇒ P/3 = Q

⇒ P : Q = 3 : 1

Total work = 9P + 8Q = 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

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