Q.Using the same Time Allowed (10 hours) and Time Rate (₹20 per hour) as in the previous question, suppose instead the worker completes the job in only 4 hours. Calculate the Bonus and Total Earnings under both Halsey and Rowan, state which scheme now gives the higher earnings, and explain why the result has reversed compared with the previous question.

Saving 6 out of 10 allowed hours is 60% of Time Allowed — past the 50% crossover point — so Rowan's bonus has already begun declining from its peak while Halsey's keeps climbing in a straight line, and Halsey now pays more.

Time Saved = 10 − 4 = 6 hours (60% of Time Allowed — above the 50% crossover point).

Halsey Bonus = 50% × 6 × 20 = ₹60; Total = (4×20)+60 = ₹140.

Rowan Bonus = (6÷10) × 4 × 20 = 0.6×80 = ₹48; Total = 80+48 = ₹128. …

Time Saved = 10 − 4 = 6 hours, which is 60% of the Time Allowed — past the 50% crossover point, so Halsey is now expected to pay the larger bonus.

Halsey Scheme:

Bonus = 50% × 6 × ₹20 = ₹60.

Basic Wages = 4 × ₹20 = ₹80.

Total Earnings = 80 + 60 = ₹140.

Rowan Scheme:

Time-Saved Ratio = 6 ÷ 10 = 0.60.

Bonus = 0.60 × 4 × ₹20 = ₹48.

Basic Wages = 4 × ₹20 = ₹80.

Total Earnings = 80 + 48 = ₹128.

Why the comparison reversed: in the previous question, only 20% of Time Allowed was saved (below the 50% crossover), so Rowan's ratio-weighted bonus was larger. Here, 60% of Time Allowed is saved — PAST the point (exactly 50% time saved, i.e. Time Taken = 5 hours here) at which the Rowan bonus reaches its maximum. Beyond that point the Rowan bonus starts to fall even as time saved keeps rising, while Halsey's bonus has no such ceiling and keeps climbing in a straight line with every additional hour saved. That is precisely why Halsey (₹140) now exceeds Rowan …

Students sometimes expect the SAME scheme to always win regardless of how much time is saved, missing that the comparison genuinely depends on where the time-saved percentage falls relative to the 50% crossov …