Given:

• 17 laborers can dig a ditch 26 meters long in 18 days, working 8 hours a day.

First, calculate the total man-days required for this task: Total man-days = (Number of laborers) × (Number of days) = 17 × 18 = 306 man-days.

Now, we want to find out how many more laborers are needed if they work 9 hours a day. Let's denote the number of additional laborers needed as "x."

In this case, the total man-days required to complete the same task with 9 hours of work per day would remain the same (306 man-days).

So, we can set up the equation: (17 + x) laborers × 9 hours per day = 306 man-days

Now, solve for x:

17x + 9x = 306 26x = 306 x = 306 / 26 x = 51

So, 51 more laborers are needed if they work 9 hours a day to complete the same task.

The correct answer is 51.