Question

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

Answer 1

Hint: We convert the mixed fraction to proper fraction. Use a unitary method to find the length of trench dug by 1 man in a day. Again use a unitary method to find the number of men required to dig 27 meters.
* Unitary methods help us to find the value of multiple objects if we are given the value of one object by just multiplying the value of a single object to the number of objects.

Complete step-by-step answer:
First we convert the mixed fraction \[6\dfrac{3}{4}\]into proper fraction
 \[ \Rightarrow 6\dfrac{3}{4} = \dfrac{{6 \times 4 + 3}}{4}\]
\[ \Rightarrow 6\dfrac{3}{4} = \dfrac{{27}}{4}\]
We are given that 11 men can dig \[\dfrac{{27}}{4}\] meter long trench in one day
Use unitary method to find the length dug by 1 man in a day
\[\because \]Length dug by 11 men\[ = \dfrac{{27}}{4}\]
\[ \Rightarrow \]Length dug by 1 man\[ = \dfrac{{27}}{{4 \times 11}}\]
\[ \Rightarrow \]Length dug by 1 man\[ = \dfrac{{27}}{{44}}\].........… (1)
Now find the number of men required to dig 27 meters of trench when we have length dug by 1 man in a day from equation (1).
Use a unitary method to find the number of men required for 1 meter of trench.
\[\because \]Number of men required to dig \[\dfrac{{27}}{{44}}\] meters of trench\[ = 1\]
\[ \Rightarrow \]Number of men required to dig 1 meter of trench \[ = \dfrac{{44}}{{27}}\]
Now we use a unitary method to calculate the number of men required to dig 27 meters of trench.
\[ \Rightarrow \]Number of men required to dig 27 meter of trench\[ = \dfrac{{44}}{{27}} \times 27\]
Cancel same factors from numerator and denominator
\[ \Rightarrow \]Number of men required to dig 1 meter of trench\[ = 44\]

\[\therefore \]Number of men required to dig 27 meters of trench is 44.

Note: * Unitary methods help us to find the value of a single by dividing the value of multiple objects by the number of objects and helps us to find the value of multiple objects by multiplying the value of a single object to the number of objects.
* General form of a mixed fraction is \[a\dfrac{b}{c}\] and it can be converted into proper fraction as \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]