Question

11 men can dig 634 meter long trench in one day. How many men should be employed for digging 27 meter long trench of the same type in one day?

Answer 1

Answer:

Let us first convert the mixed fraction to a improper fraction.

$\implies 6 \dfrac{3}{4} = \dfrac{27}{4}\:m$

So it is given that, 11 men can dig 27/4 m in a day. So we are required to calculate the number of extra men needed, if 27 m was to be dug within a day.

Since the addition of extra labour will cause in decrease of number of days, the given relation is directly proportional. Hence applying the given information in terms of ratio we get:

$\implies 11 : \dfrac{27}{4} :: x : 27$

Product of Means = Product of Extremes

$\implies 27 \times 11 = \dfrac{27}{4} \times x\\\\\\\implies 297 = \dfrac{27 x}{4}\\\\\\\implies x = \dfrac{297 \times 4}{27}\\\\\\\implies x = 11 \times 4\\\\\\\implies \boxed{ \bf{ x = 44}}}$

Hence if 33 more men are added to the present number of workers, the digging work of 27 m can be completed within a day.