64 persons can dig a trench 50m long, 2m wide, and 2m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75m long, 4m wide, and 3m deep?

Question: 64 persons can dig a trench 50m long, 2m wide, and 2m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75m long, 4m wide, and 3m deep?

Solution:
The volume of 50m long, 2m wide, and 2m deep is (50 × 2 × 2) m³ = 200 m³
The volume of 75m long, 4m wide, and 3m deep is (75 × 4 × 3) m³ = 900 m³

64 persons by working 12 hours daily can dig 200m³ in = 5 days.
∴ 1 person by working 1 hour daily can dig 1 m³ in = (5 × 64 × 12)/200 days.
∴ 80 persons by working 8 hour daily can dig 900 m³ in = (5 × 64 × 12 × 900)/(200 × 80 × 8) days.
= 27 days