Consider the following graph:

Which one of the following statements is not correct with reference to the graph given above?

The correct answer is: "During the period from 1st April to 1st September, at no time was the actual progress more than the expected progress."

By analyzing the provided graph, we can evaluate each statement step-by-step to determine which one is not correct:

1. Understanding the Graph Components:
- Y-axis: Represents the percentage of work completed (labeled as % of work), ranging from 0% to 100%.
- X-axis: Represents the timeline, with major milestones marked at 1st April, May, June, July, Aug, and 1st Sept.
- Expected Progress (Dashed Line): Shows the planned progress curve over time.
- Actual Progress (Solid Line): Shows the real progress achieved over time.

2. Analyzing Statement 1: "On 1st June, the actual progress of work was less than expected."
Locate the vertical line for June (1st June) on the x-axis:
- The expected progress (dashed line) is at the 50% level:
$50\%$
- The actual progress (solid line) is at approximately the 20% level:
$20\%$
Since the actual progress (20%) is less than the expected progress (50%), this statement is correct.

3. Analyzing Statement 2: "The actual rate of progress of work was the greatest during the month of August."
The rate of progress corresponds to the slope (steepness) of the actual progress curve (solid line):
- Between Aug and 1st Sept, the solid line rises sharply from about 42% to 100% in a very short span of time.
- This segment is the steepest portion of the solid curve across the entire graph, meaning the rate of work was highest during this period. Thus, this statement is correct.

4. Analyzing Statement 3: "The work was actually completed before the expected time."
- The expected completion time (when the dashed line reaches the 100% work mark) is exactly on 1st Sept.
- The actual completion time (when the solid line reaches the 100% work mark) occurs before 1st Sept (the solid line hits the 100% horizontal line to the left of the 1st Sept vertical line).
- Therefore, the work was completed ahead of schedule, making this statement correct.

5. Analyzing Statement 4: "During the period from 1st April to 1st September, at no time was the actual progress more than the expected progress."
- If we look at the region in August just before completion, the solid line (actual progress) crosses above the dashed line (expected progress) as it rushes to reach 100%.
- During this specific window, the actual progress was higher than the expected progress.
- Therefore, the claim that at "no time" was actual progress more than expected progress is not correct.