Question : A and B working separately can complete a piece of work in 10 and 16 days, respectively. If they work for a day alternately, with A beginning the work, in how many day (s) will the work be completed?
Option 1: $10 \frac{1}{4}$
Option 2: $12 \frac{1}{4}$
Option 3: $1\frac{1}{4}$
Option 4: $\frac{1}{4}$
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Correct Answer: $12 \frac{1}{4}$
Solution :
Let the total work be 80 units
The efficiency of A and B = $\frac{80}{10}$ units/day, $\frac{80}{16}$ units/day respectively
⇒ The efficiency of A and B = 8 units/day, 5 units/day respectively
Effective efficiency of A and B together = 8 + 5 = 13 units/day
According to the question,
They work on alternative days.
⇒ Work completed in 2 days = 13 units
In 12 days work completed = 78 units
Now, the remaining 2 units will be completed by A in $\frac{2}{8}$ days or $\frac{1}{4}$ days.
⇒ Total time = $12 + \frac{1}{4}=12\frac{1}{4}$ days
Hence, the correct answer is $12\frac{1}{4}$.
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