Question

600 soldiers in a fort had enough food for 14 days. after 4 days , some soldiers were transferred to another fort and thus the food lasted for 30 more days. how many soldiers left the fort?​

Answer 1

R D Sharma - Mathematics 9

After 6 days, for 600 soldiers food would last for (30 - 6) = 24 days. Given that food lasted for 40 days. ⇒ x = 240. Therefore, the number of soldiers left the fort is 240.

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Answer 2

$Let \: Number \: of \: Soilders \: be \: \\ left \: in \: the \: fort \: be \: x$

$After \: 6 \: days , \: For \: 600 \: \: \\ Soldiers \: will \: be \: (14 -4) =10$

$Inverse \: Proportion :$

$600 \times 10 =40 (600 - x)$

$6,000 = 24,000 - 40x$

$6,000 - 24,000 = - 40x$

$- 18,000 = - 40x$

$x = \frac{ - 18,000}{ - 40}$

$x = 450$