Question : A can do a work in 6 days, which B alone can do in 8 days. In how many days they together can do it?
Option 1: $\frac{24}{7}$ days
Option 2: $\frac{25}{7}$ days
Option 3: $\frac{27}{4}$ days
Option 4: $\frac{22}{3}$ days
Correct Answer: $\frac{24}{7}$ days
Solution :
One day's work of A = $\frac{1}{6}$
One day's work of B = $\frac{1}{8}$
One day's work of A and B together = $\frac{1}{6}+\frac{1}{8}$ = $\frac{4+3}{24}$ = $\frac{7}{24}$
$\therefore$ Together they can complete the work in ($1÷\frac{7}{24}$) = $\frac{24}{7}$ days
Hence, the correct answer is $\frac{24}{7}$ days.
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