Q.For a job with Time Allowed = 10 hours and Time Rate = ₹20 per hour, compute the Rowan Bonus for Time Taken = 3, 4, 5, 6 and 7 hours, and show that the Bonus is at its maximum when Time Taken equals exactly half of the Time Allowed.

Working out the Rowan bonus at several different Time-Taken values on the same job shows the bonus rising, peaking, and then falling as time taken keeps shrinking — exactly the self-limiting behaviour Rowan is designed to have.

Bonus = (Time Saved ÷ Time Allowed) × Time Taken × Time Rate, with Time Allowed = 10 hours and Time Rate = ₹20, computed for each Time Taken value:

The Bonus rises steadily as Time Taken falls from 3 to 5 hours (₹42 → ₹48 → ₹50), then FALLS by the exact mirror-image amounts as Time Taken keeps falling further, from 5 to 7 hours (₹50 → ₹48 → ₹42). The maximum, ₹50, occurs precisely at Time Taken = 5 hours — exactly half of the 10-hour Time Allowed (i.e., exactly 50% of the time has been saved) — and the table is perfectly symmetric around that point (Time Taken = 4 and 6 hours both give ₹48; Time Taken = 3 and 7 hours both give ₹42). This confirms, with real figures, the self-limiting property stated in Section 4.B: saving MORE …

The same peak can be located without building the whole table: since Bonus = ((Time Allowed − Time Taken) ÷ Time Allowed) × Time Taken × Time Rate, the two factors that multiply Time Taken — the shrinking Time-Saved Ratio and the shrinking Time Taken itself — pull in opposite directions as Time Taken f …

Students sometimes assume that saving MORE time must always mean a LARGER Rowan bonus, since that is true under Halsey — this table is the direct numerical proof that the a …