Question

a garrison with 100 soldiers have sufficient food for 30 days if 50 more soldiers from the camp find the number of days for which the stored food will last​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• A garrison with 100 soldiers have sufficient food for 30 days

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Number of days the food would last if 50 more soldiers are added

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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• Let the number of days the food would last if 50 more soldiers are added be "d"

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As the total food will remain same hence we will calculate the total food available

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Case I

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$\underline{\bold{\texttt{Total food :}}}$

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Number of soldiers × Number of days the food will last

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• Number of soldiers = 100

• Number of days the food will last = 30

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➜ 100 × 30

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➜ 3000 units ⚊⚊⚊⚊ ⓵

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Case II

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$\underline{\bold{\texttt{Total food :}}}$

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Number of soldiers × Number of days the food will last

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• Number of soldiers = 100 + 50 = 150

• Number of days the food will last = d

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➜ 150 × d

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➜ 150d units ⚊⚊⚊⚊ ⓶

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As discussed above the total food will be same

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Thus ,

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Equation ⓵ = Equation ⓶

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➜ 3000 = 150d

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➜ $\sf d = \dfrac { 3000 } { 150 }$

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➨ d = 20

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• Hence if 50 more soldiers are added then the food will last for 20 days

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