If 10 persons can dig 8 feet trench in 12 days

If 10 persons can dig 8 feet trench in 12 days, then how many days will 8 persons take to dig 6 feet trench?

  1. 10 days
  2. 10.25 days
  3. 11 days
  4. 11.25 days

Answer

Here, we can define work in terms of man - days. Also, the work required will be proportional to the depth of trench required.

So, 12 × 10 men - days of work is required to dig 8 feet of trench or

Also, let x be the days required for digging 6 feet of trench by 8 men.

So, x × 8 men - days of work is required to dig 6 feet of trench. 

So, 1 feet of trench digging requires (12 × 10) / 8 men - days = (x × 8) / 6 men - days

So, x = ((12 × 10) / 8) × 6 / 8 = 45 / 4 = 11.25 days

The correct option is D.