Question

A fort has enough food for 720 soldiers for 35 days. If after 5 days 120 soldiers leave the fort, how long will the food last now ?

quality answers accepted.

Answer 1

$Number \:of \: soldiers \: and \: their \: food \\stock \: are \: in \: inverse \: proportion .$

$\begin {tabular} {|c|cc| } </p><p>\cline {1-3} Number soldiers (x) & 720&720-120 = 600 \\</p><p>\cline {1-3} Number of days (y) & 35&y_{2} \\</p><p>\cline {1-3} </p><p>\end {tabular}$

$Here , x_{1} = 720 , \: x_{2} = 600 \\y_{1} = 35, \: y_{2} = ?$

$x_{2} \times y_{2} = x_{1} \times y_{1}$

$\implies 600 \times y_{2} = 720 \times 35$

$\implies y_{2} = \frac{720 \times 35}{600}\\= 6 \times 7 \\= 42 \: days$

Therefore.,

$\red { The \: food \:will \:be \: stock \:for }\\\red{(720-120) = 600 \: soldiers }\green {=42 \: days }$

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Answer 2

Answer:

Here,x

1

=720,x

2

=600

y

1

=35,y

2

=?

x_{2} \times y_{2} = x_{1} \times y_{1}x

2

×y

2

=x

1

×y

1

\implies 600 \times y_{2} = 720 \times 35⟹600×y

2

=720×35

\begin{gathered}\implies y_{2} = \frac{720 \times 35}{600}\\= 6 \times 7 \\= 42 \: days \end{gathered}

⟹y

2

=

600

720×35

=6×7

=42days

Therefore.,

\begin{gathered} \red { The \: food \:will \:be \: stock \:for }\\\red{(720-120) = 600 \: soldiers }\green {=42 \: days } \end{gathered}

Thefoodwillbestockfor

(720−120)=600soldiers=42days