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P, Q, and R take 1 day to complete a work. If P works alone, he finishes the work in 2 days and if Q works alone he finishes it in 3 days. How long will it take R to complete the work alone?

P, Q, and R take 1 day to complete a work. If P works alone, he finishes the work in 2 days and if Q works alone he finishes it in 3 days. How long will it take R to complete the work alone? Correct Answer 6 days

Given

P, Q and R complete works in 1 day when work together.

Calculation

P completes work in 2 days.

Work done by P in 1 day = 1/2

Q completes work in 3 days.

Work done by Q in 1 day = 1/3

Let R completes work in x days

Work done by R in 1 day = 1/x

According to question

(1/2) + (1/3) + (1/x) = 1

(3 + 2)/6 + (1/x) = 1

(5/6) + (1/x) = 1

(1/x) = 1 - (5/6)

(1/x) = (1/6)

x = 6

R completes work in 6 days.

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