Question

A garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?
Give a detailed explanation.​

Answer 1

Answer:

$x { }^{2} + 10x + 24$

Answer 2

$\underline{\underline{\red{\sf Given:}}}$

• Total no. of men = 500
• 500 men had Provisions for = 27days
• After 3days reinforcement of 300men arrived

$\underline{\underline{\red{\sf Find:}}}$

• For how many more days will the remaining food last for = ?

$\underline{\underline{\red{\sf Solution:}}}$

Let, the remaining food will last for x days

Now, 500men had Provisions for

= 27 - 3 = 24 days

Now,

$\sf (500 + 300)men \: had \: provision \: for \: x \: days$

We, know that more men less days

$\sf\therefore \frac{800}{500} = \frac{24}{x}$

$\sf\implies 800 \times x = 500 \times 24$

$\sf\implies 800 \times x = 12000$

$\sf\implies x = \frac{120\cancel{00}}{8\cancel{00}}$

$\sf\implies x = \frac{120}{8}$

$\sf\implies x = \frac{\cancel{120}}{\cancel{8}} = 15$

$\sf\implies x =15days$

Hence, The remaining food will last for 15days