Question : If A can do a work in 21 days and B can do the same work in 28 days. In how many days will they complete the work if they work on alternate days?
Option 1: 22 days
Option 2: 28 days
Option 3: 20 days
Option 4: 24 days
Correct Answer: 24 days
Solution :
Time taken by A to do the work = 21 days
Part of work done by A in a day = $\frac{1}{21}$
Time taken by B to do the work = 28 days
Part of work done by B in a day = $\frac{1}{28}$
Part of work done by A and B in first 2 days = $\frac{1}{21}$ + $\frac{1}{28}$ = $\frac{4+3}{84}$ = $\frac{1}{12}$
Time taken by A and B to work on alternative days = 2 × 12 = 24 days
Hence, the correct answer is 24 days.
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