A can complete a work in 16 days, working 6 hours a day. B can complete the same work in 12 days, working 9 hours a day. If both A and B work together, working 8 hours a day, in how many days can they complete the work?

108/17

The correct answer is Option (1) → 108/17

Let the total work = 1 unit.

Step 1: Find hourly work rates

A:

• Completes work in 16 days × 6 hours/day = 96 hours
• Hourly work rate of A = $\frac{1}{96}$​

B:

• Completes work in 12 days × 9 hours/day = 108 hours
• Hourly work rate of B = $\frac{1}{108}$​

Step 2: Combined hourly work rate

$\frac{1}{96} + \frac{1}{108}$​

LCM of 96 and 108 = 864

$= \frac{9}{864} + \frac{8}{864} = \frac{17}{864}$

So, together they do $\frac{17}{864}$​ work per hour.

Step 3: Daily work when working 8 hours/day

$\text{Daily work} = 8 \times \frac{17}{864} = \frac{17}{108}$

Step 4: Time required to complete the work

$\text{Days} = \frac{1}{17/108} = \frac{108}{17}$