Question
Download Solution PDFA and B can complete a piece of work in 13 and 17 days respectively. A begins to do the work, and they work alternatively one at a time for one day each. The whole work will be completed in:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time in which A can complete a piece of work = 13 days
Time in which B can complete a piece of work = 17 days
Concept used:
L.C.M. of 13 and 17 = 221
Thus, total work done = 221 units.
Unit of work done by A in 1 day = 17 units
Unit of work done by B in 1 day = 13 units
Calculation:
If A and B work alternatively, work done by them in 2 days = 30 units
Work done in 14 days = 30 × 7 = 210 units
Work left = 11 units
Work done remaining by A on 15th day = \(11 \over 17\)
Thus, the time taken to complete the work = 14\(11 \over 17\) days.
∴ The whole work will be completed in 14\(\bf 11 \over 17\) days.
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