11. If 75 men can dig a trench 300 m long, 9 m wide and 3 m

deep in 6 days working 5 hours a day, in how many days

will 50 men dig another trench 540 m long, 6 m wide and

4.5 m deep working 4 hours a day ?

Solution: Such questions are best solved by work equivalence method

Work done has two facets - the input side and the output side -

On the input side is the effort of the group of men and on the output side is the output - which in this case is the trench measured in terms of its volume.

Thus we have the first equation

75 x 6 x 5 = k. 300 x 9 x 3 (Note: we multiplied the RHS by K to ensure equality of units on both sides - which is the role of any constant of proportionality)

The second equation => 50 x z days x 4 =k. 540 x 6 x 4.5 ------2

On dividing equation 1 by 2 , k, the constant of proportionality will be eliminated and we will get the value of z = 20.25

On the first glance this method looks time consuming. But this method is the most efficient way of solving this question- this is even more efficient than the chain rule method - for a simple reason that this method is mechanical. With some practice you can instinctively reach the last step in no time.