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Answer:

[tex]\boxed{\bf \: 55\:more \: men \: are \: required \: } \\ [/tex]

Step-by-step explanation:

Given that, 5 people can eat a certain amount of rice in 30 days.

Now, we have to find how many more men are needed to finish the same quantity of rice in 10 days.

We know, more persons, less number of days are needed.

So, it means, number of days and number of men required are in inverse variation.

Let assume that number of more men required be x.

So, we have

[tex]\begin{array}{|c|c|c|} \\ \rm Number \:of\:men \:\: &\rm 5 \: &\rm 30\: \: \\ \\ \rm Number \: of \: days \: &\rm 5 + x&\rm 10 \\ \end{array} \\ \\[/tex]

So, using law of inverse variation, we have

[tex]\sf \: 5 \times (5 + x) = 30 \times 10 \\ [/tex]

[tex]\sf \:5 + x = 6 \times 10 \\ [/tex]

[tex]\sf \:5 + x = 60 \\ [/tex]

[tex]\sf \:x = 60 - 5 \\ [/tex]

[tex]\qquad\sf\implies \sf \:x = 55 \\ [/tex]

Hence,

[tex]\sf\implies \sf \: 55\:more \: men \: are \: required \\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]

Answer:

Extra number of men required = 51 – 30 = 21 men

Step-by-step explanation:

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