Question : A can do a piece of work in 9 days, while B can do it in 12 days. A and B together can do the work in:
Option 1: $5\frac{1}{7}$ days
Option 2: $5\frac{2}{7}$ days
Option 3: $6\frac{1}{7}$ days
Option 4: $6\frac{2}{7}$ days
Correct Answer: $5\frac{1}{7}$ days
Solution :
Given: A can do a piece of work in 9 days, while B can do it in 12 days.
So, in 1 day A and B can do $\frac{1}{9}$th part and $\frac{1}{12}$th part of the work, respectively.
Now together in 1 day they can do ($\frac{1}{9}$ + $\frac{1}{12}$) = $\frac{12+9}{108}$ = $\frac{21}{108}$th part of the work
$\therefore$ A and B together can do the work in (1÷$\frac{21}{108}$) = $\frac{108}{21}$ = $\frac{36}{7}$ = $5\frac{1}{7}$ days
Hence, the correct answer is $5\frac{1}{7}$ days.
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