I. If X and Y work alternately starting with X, then the piece of work will be finished on the fifth day.
II. If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.
Select the answer using the code given below :
I only
To solve this question, we need to evaluate each statement based on the given conditions. Let's assess each statement step-by-step:
Given:
- X can finish the work in 4 days.
- Y can finish the same work in 6 days.
Calculations:
- Work done by X in 1 day \(= \frac{1}{4}\).
- Work done by Y in 1 day \(= \frac{1}{6}\).
Let's calculate the work done when they work alternately:
- Statement I: If X and Y work alternately starting with X, then the piece of work will be finished on the fifth day.
- Days 1 and 2: Combination of 1 day of work by X and 1 day of work by Y.
Work done in 2 days \(= \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}\). - Days 3 and 4: Another combination of 1 day of work by X and 1 day of work by Y repeat.
Additional work done \(= \frac{5}{12}\).
- Days 1 and 2: Combination of 1 day of work by X and 1 day of work by Y.
- Additional work done by X on the 5th day \(= \frac{1}{4}\).
- \(= \frac{5}{6} + \frac{1}{4} = \frac{10}{12} + \frac{3}{12} = 1\).
- Statement II: If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.
- Days 1 and 2: 1 day of work by Y, followed by 1 day of work by X.
Work done in 2 days \(= \frac{1}{6} + \frac{1}{4} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12}\). - Days 3 and 4: The same pattern repeats.
Additional work done \(= \frac{5}{12}\).
- Days 1 and 2: 1 day of work by Y, followed by 1 day of work by X.
- Additional work done by Y on the 5th day \(= \frac{1}{6}\).
- \(= \frac{5}{6} + \frac{1}{6} = 1\).
Final Conclusion: The correct answer is "
I only
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