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Question

11 men can dig $$ 6\dfrac{3}{4}$$ metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day?


Solution

Let $$x$$ be the number of men required to dig a trench of $$27$$ meter.
Number of men$$11$$ $$x$$ 
Length ( in m ) $$6\dfrac{3}{4}=\dfrac{27}{4}$$$$27$$
Since, the length of the trench and the number of men are in direct variation, we have:
$$\Rightarrow$$  $$\dfrac{11}{x}=\dfrac{27/4}{27}$$

$$\Rightarrow$$  $$11\times 27=x\times \dfrac{27}{4}$$

$$\Rightarrow$$  $$x=\dfrac{11\times 27\times 4}{27}$$

$$\Rightarrow$$  $$x=44$$

$$\therefore$$  $$44$$ men will be required to dig a trench of $$27$$ meter. 

Mathematics

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