Question

If 12 persons working 12 hours a day dig 12 meters of a tunnel in 12 days, how many men are required to dig additional 04 meters of the tunnel (of the same dimension) given that they work 04 hours a day for 04 days

Answer 1

To work out this question, you will have to find the amount of the tunnel that 1 man can dig in 1 hour:

If 12 people dig 12 meters in 12 days

That means that they dig, 12 meters/12 days = 1 meter every day

If the 12 may dig 1 meter per day in 12 hours, that means in 1 hour they dig:

1 meter / 12 hours = 1/12 meters per hour

If 12 of the men dig 1/12 meters of the tunnel in 1 hour,  1 man digs:

1/12 ÷ 12 = 1/12 × 1/12 = 1/144 of the tunnel in 1 hour.

How many men are required to dig additional 04 meters of the tunnel (of the same dimension) given that they work 04 hours a day for 04 days?

To answer this let us work out from the fraction that 1 man digs in hour(1/144 meters)
 

4 meters of the tunnel = 12 m + 4 m = 16 meters.

The section of the tunnel which will be dug per day working 4 days = 16m / 4 = 4meters every day

The men will be required to work 4 hours per day. Therefore they will dig 4/4 = 1 meter per day

If 1 man digs 1/144 m = 1 hour
To dig 1 meter in 1 hour, then men will need to be:
If 1/144m = 1 man
Then 1 m = 1 x 1 ÷1/144      
                  = 1 × 144
                  = 144 men

Therefore 144 men are required to dig 16 meters of the tunnel working 4 hours per day in 4 days