Question : A alone can complete a work in 16 days and B alone can complete the same work in 96 days. In how many days both A and B together can complete the same work?
Option 1: $\frac{88}{13}$ days
Option 2: $\frac{96}{7}$ days
Option 3: $\frac{96}{13}$ days
Option 4: $\frac{88}{14}$ days
Correct Answer: $\frac{96}{7}$ days
Solution :
One day's work of A = $\frac{1}{16}$
One day's work of B = $\frac{1}{96}$
One day's work of A and B together
= $\frac{1}{16}+\frac{1}{96}$
= $\frac{6+1}{96}$
= $\frac{7}{96}$
$\therefore$ Together they can complete the work in $\frac{96}{7}$ days.
Hence, the correct answer is $\frac{96}{7}$ days.
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