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P, Q and R are working on a project. P can complete the work alone in 10 days, Q completes the work alone in 15 days and R completes the work alone in 18 days. But Q leaves the project 5 days before the completion of the project and R leaves after 3 days, when Q leaves. Find the total time required to complete a project.

P, Q and R are working on a project. P can complete the work alone in 10 days, Q completes the work alone in 15 days and R completes the work alone in 18 days. But Q leaves the project 5 days before the completion of the project and R leaves after 3 days, when Q leaves. Find the total time required to complete a project. Correct Answer 6.5 days

Given:

P can complete the work = 10 days

Q completes the work = 15 days

R completes the work = 18 days

Calculation:

Let work completes in x days.

Q works for (x – 5) days

P works for x days

R works for (x – 5 + 3) days

= (x – 2) days

According to question:

(x/10) + (x - 6)/15 + (x - 3)/18 = 1

⇒ {9x + 6(x - 5) + 5(x - 2)}/ 90 = 1

⇒ 9x + 6x – 30 + 5x – 10 = 90

⇒ 20 x – 40 = 90

⇒ 20x = 90 + 40

⇒ 20x = 130

⇒ x = 6.5 days

∴ Total time required to complete the project is 6.5 days.

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