Correct Answer - Option 1 : 66 / 7 days
Given∶
X completes a work in 11 days
Y completes a work in 66 days
Calculation∶
X’s 1 day work = (1 / 11)
Y’s 1 day work = (1 / 66)
Work done by X and Y in 1 day = (1 / 11) + (1 / 66)
⇒ (6 + 1) / 66
⇒ 7 / 66
∴ 66 / 7 days are required if X and Y works together.