Correct Answer - Option 3 : 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.