Question

a fort had provisions for 150 mens for 45 days after 10 days 25 men left the fort how long will the food last at the same time

Answer 1

150 men had provisions for (45-10)days
1 man had provisions for = 150*35days = 5250 days
150-25 = 125 men had provisions for = 5250/125 = 42 days
hope it was helpful

Answer 2

${\large{\bold{\rm{\underline{Given \; that}}}}}$

✯ Fort had provisions for 150 men for 45 days

✯ After 10 days, 25 men left the fort.

${\large{\bold{\rm{\underline{To \; find}}}}}$

✯ How long will the food last at the same rate?

${\large{\bold{\rm{\underline{Solution}}}}}$

✯ How long will the food last at the same rate? 54

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ The question is from a very interesting chapter of mathematics named, Propositions..! There are two types of proposition's namely, Direct and Inverse proportion..! Let's see this question is from which topic of proposition..!

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

~ The number of people's increase, food will get over fast fast. If the number of people's decrease, food will over slowly slowly means it take a long time to be over..!

Henceforth, it is cleared that the question is from topic "Inverse proportion"..!

For 150 men for 45 days. after 10 days, 25 men left the fort, the food last at the same rate..!

↝ Remaining people' = 150-25

↝ Remaining people' = 125

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

~ There are two method's to solve this inverse proportion let's solve it by easier method but intersting..!

Let the days be x

↝ 150 men : 45 days :: 125 men : x

↝ 150 × 45 = 125 × x

↝ 6750 = 125 × x

↝ 6750 = 125x

↝ 6750/125 = x

↝ 54 = x

↝ x = 54

Henceforth, the food last at the same be 54 days...!

${\large{\bold{\rm{\underline{Knowledge}}}}}$

Addítíσnαl ínfσrmαtíσn, thє ínfσrmαtíσn ís rєlαtєd tσ thє tσpíc - "Prσpσrtíσn's" !

♛ Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. That's if ${\sf{\dfrac{x}{y} = k}}$ [ k is a positive number ], then x and y are said to vary directly. In such a case if ${\sf{y_{1} \: , y_{2}}}$ are the values of y corresponding to the value ${\sf{x_{1} \: , x_{2}}}$ of x respectively then, ${\sf{\dfrac{x_{1}}{y_{1}} \: = \: \dfrac{x_{2}}{y_{2}}}}$

♛ Two quantities x and y are said to be inverse proportion if an increase in x causes a proportional decrease in y (vice - versa !) in such a manner that the product of their corresponding values remains constant. That is if xy = k, then x and y are said to vary inversely. In this case if ${\sf{y_{1} \: , y_{2}}}$ are the values of y corresponding to the values ${\sf{x_{1} \: , x_{2}}}$ of x respectively then ${\sf{x_{1} y_{1}}}$ = ${\sf{x_{2} y_{2}}}$ or ${\sf{\dfrac{x_{1}}{x_{2}} \: = \: \dfrac{y_{2}}{y_{1}}}}$