Question : X and Y can complete a work in 9 days and 36 days, respectively. X begins to do the work and they work alternately one at a time for one day each. The whole work will be completed in:
Option 1: $12\frac{1}{2}$ days
Option 2: $14\frac{1}{4}$ days
Option 3: $13\frac{1}{3}$ days
Option 4: $15\frac{1}{5}$ days
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Correct Answer: $14\frac{1}{4}$ days
Solution : Let total Work = LCM (9, 36) = 36 units The rate of work done by X in 1 day = 4 units The rate of work done by Y in 1 day = 1 unit The combined work done by both X and Y works alternately for one day each = 5 units So, 35 units of work be done in 14 days. Remaining 1 unit work be done by X in $\frac{1}{4}$ days So, total time taken = $14\frac{1}{4}$ days Hence, the correct answer is $14\frac{1}{4}$ days.
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