Question

a garrison of 200 men has provisions for 45 days . if 50 more men join the garrison then find the number of days for which the food will last.

Answer 1

If two quantities x and y are in
Inverse variation then
x × y = k ( constant )


200 men had provisions for 45 days.


After 15 days ,
200 men had provisions for 30days.
Now ,


i ) Number of men ( x1 ) = 200
Provisions finished ( y1 ) = 30 days



ii ) after 15 days number of men
joined are 40.


Therefore,
Number of men
after 15 days ( x2 ) = 240
Let food last in Number of days = y2
x2 × y2 = x1 × y1
y2 = ( x1 × y1 ) / x2
y2 = ( 200 × 30 ) / 240
= 25


Therefore,
Remaining food will last in 25days.
I hope this helps you.

Answer 2

If 50 more men join then the food will last for 36 days only.

Step-by-step explanation:

Here in the question it is given that 200 men have provision for 45 days only.

⇒So, if only one man is there then the food will last for =(total no. of men)×(total days of provision)

⇒So, for one man the food will last for=200×45=9000 days

⇒So, if 50 more men join then the total number of men will be=250 men

⇒The number of days for which the provision will last =(Food available for one man÷ Total men available)

⇒(9000)÷(250)=36 days(answer)