Twelve persons working 16 hours per day earn ₹ 33,600 in a week (same weekly span). At the same rate, how much will eighteen persons earn working 12 hours per day in a week?

Introduction: Earnings at a constant hourly rate scale with total person-hours (persons × hours/day × days). If the “week” length is unchanged across scenarios, comparing person-hours suffices. We can compute a per person-hour rate and then apply it to the new configuration.

Given Data / Assumptions:

• Base earnings: ₹ 33,600 for 12 persons × 16 h/day × 1 week.
• New scenario: 18 persons × 12 h/day × same week duration (same number of days).
• Rate per person-hour is constant.

Concept / Approach: Per person-hour rate r = 33,600 / (12 * 16 * 7) if days are to be explicit; equivalently, we can use proportional comparison since the week length cancels. Using ratios is quicker: Amount ∝ persons × hours/day × days (days fixed).

Step-by-Step Solution:

Verification / Alternative check: Compute per person-hour rate: 33,600 / (12*16) = 175 per day-basis; multiply by 18*12 = 216 to get 37,800 per day equivalently for the same number of days. Consistent either way.

Why Other Options Are Wrong: ₹ 40,000, ₹ 35,000, ₹ 28,800, or staying at ₹ 33,600 do not match the exact 12.5% increase in person-hours (from 192 to 216).

Common Pitfalls: Assuming linear scaling with persons only and ignoring the hours change; always incorporate both people and hours when computing proportional earnings.

Final Answer: ₹ 37,800