Twenty women finish a work in 16 days; sixteen men finish the same work in 15 days. What is the ratio of the efficiency (capacity) of a man to that of a woman?

Problem restatementCompare per-day productivity of a typical man versus a typical woman using the same total work.

Given data

• 20 women × 16 days = 1 job.
• 16 men × 15 days = 1 job.

Concept/ApproachLet one woman's rate be w and one man's rate be m (jobs/day). Equate total work.

Step-by-step calculation 20w × 16 = 16m × 15 320w = 240m Divide by 80: 4w = 3m → m = (4/3)w

Therefore, man : woman efficiency = m : w = 4 : 3.

VerificationIf w = 3 units, then m = 4 units (arbitrary scale). Totals match the equality 320w = 240m.

Common pitfalls

• Inverting the ratio (writing 3 : 4 instead of 4 : 3).

Final Answer4 : 3