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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


Team Careers360 7th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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