Question

A fort had provisions for 150 men for 45 days. after 10 days, 25 men left the fort . how long will the food last at the same rate.{ please full explain}

Answer 1

Answer:

This is a question of Inverse Proportion.

That is,

If number of people increase, food gets over quickly. If number of people decrease, then food lasts for a longer time.

Now, it is given that,

For 150 men, food lasted 45 days. After 10 days, if 25 men left the fort, how many days will the food last.

Since 25 men, left the camp after 10 days, the remaining people would be:

⇒ Remaining People = 150 - 25 = 125 people

Hence using the inverse proportion method we get:

$\implies 150\: men: 45\:days :: 125\:men :\:?\\\\\\\implies 150 \times 45 = 125 \times x\\\\\\\implies x = \dfrac{150 \times 45}{125}\\\\\\\implies x = \dfrac{6750}{125}\\\\\\\implies \boxed{ \bf{ x = 54\:days}}$

Hence the food will last for 54 days more if 25 men left the fort after 10 days.

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 ${\sf{\dfrac{x_{1}}{x_{2}} \: = \: \dfrac{y_{2}}{y_{1}}}}$