Question

a garrison of 200 men had provision of goods for 45 days. A reinforcement of 50 men arrived. Find the number of days that the food will last​

Answer 1

$\large{\underline{\underline{\sf{Given :-}}}}$

• 200 men = 45 days
• Addition of 50 men = ?

$\large{\underline{\underline{\sf{To \: Find :-}}}}$

• No. of days the food will last if 50 members are added.

$\large{\underline{\underline{\sf{Variation :-}}}}$

• Inverse variation

In inverse variation if the value of x raises the value of Y will decrease and if the value of y will increase the value of x will decrease.

With an example : If a work is done by more people the work will be done soon and if less people the work will take time.

Here let the people be x .

And time be y.

If x (people) will increase y (time) will decrease. And vice versa.

Following the same information above ; we can also conclude that if if people are more the food will last for less days and if the people are less the food will last for more days.

$\large{\underline{\underline{\sf{Solution :-}}}}$

$\longrightarrow{\sf{200\: people = 45 days }}$

$\longrightarrow{\sf{200 + 50 \: reinforcement = 250}}$

$\longrightarrow{\sf{250 = ?}}$

$\longrightarrow{\sf{\dfrac{200 \times 45}{250}}}$

$\longrightarrow{\sf{\dfrac{\cancel{200} \times 45}{\cancel{250}}}}$

$\longrightarrow{\sf{\dfrac{4 \times 45}{5}}}$

$\longrightarrow{\sf{\dfrac{4 \times \cancel{45}}{5}}}$

$\longrightarrow{\sf{4 \times 9}}$

$\large{\boxed{\underline{\implies{\sf{36\: days}}}}}$

$\large{\underline{\underline{\sf{Verification :-}}}}$

If we simplify both the sides ; they must give 1 .

$\longrightarrow{\sf{\dfrac{200 \times 45}{250 \times 36}}}$

$\longrightarrow{\sf{\dfrac{\cancel{4} \times 45}{5 \times \cancel{36}}}}$

$\longrightarrow{\sf{\dfrac{1 \times 45}{5 \times 9}}}$

$\longrightarrow{\sf{\dfrac{\cancel{45}}{5 \times</p><p> \cancel{9}}}}$

$\longrightarrow{\sf{\cancel{\dfrac{5}{5}} \implies 1}}$