Production is proportional to men × hours × days. If 15 men make 12 toys by working 5 hours per day for 16 days, in how many days can 10 men make 15 toys by working 8 hours per day (same productivity per man-hour)?

Introduction / Context:
Output in such problems scales directly with the product of number of men, hours per day, and days, assuming a constant per man-hour productivity. We set up a proportionality to relate the two scenarios.

Given Data / Assumptions:

• Scenario 1: 15 men, 5 h/day, 16 days ⇒ 12 toys.
• Scenario 2: 10 men, 8 h/day, D days ⇒ 15 toys.
• Uniform productivity k toys per man-hour.

Concept / Approach:
If k is toys per man-hour, then toys = men * hours/day * days * k. Use Scenario 1 to find k, then plug into Scenario 2 to solve for D.

Step-by-Step Solution:

Verification / Alternative check:
Proportion check: Desired toys 15 is 1.25 times 12, but man-hours per day changed; explicit calculation above is safest and consistent.

Why Other Options Are Wrong:
18 2/3 and 18 4/5 are near but do not match the exact decimal 18.75; 18 5/7 and 19 deviate further from the computed value.

Common Pitfalls:
Confusing total hours with hours per day; forgetting to include all three factors (men, hours, days) in proportion; rounding too early.

Final Answer:
18 3/4 days