20 Tonnes of rice can feed 300 soldiers for 72 days. For how many days can 32 tonnes of rice can feed 540 soldiers? Plz tell me this answer

Question

Really confused about this question please tell me its answer 

Thankyou Very Much

Answer 1

To explain it in more clearer, concise terms, a soldier needs to eat a certain amount of rice per day. Thus each soldier has a food consumption *rate* R. This is a time rate, normalized to one soldier.

 

 

Even if you have more soldiers, this per-soldier food consumption rate *doesn't change*. This rate is thus defined:

 

R = food / (days * soldiers)

 

This R is a RATE CONSTANT defined by the problem. We can solve for it by realizing that 

 

R = 20 tonnes / (300 days * 72 soldiers) 

 

If we calculate this out we get  9.26 * 10^-4 or 1/1080. You can easily confirm this by taking the inverse of R (that is, 1/R) which is (300 days * 72 soldiers) / 20 tonnes and finding that it is 1080 "soldier*days per ton".

 

Thus 1/R = 1080 soldier*days / ton

 

It is looking at the inverse of R -- 1/R -- that allows us to solve the problem. 

 

If you multiply 1/R by 32 tons, you get the amount of soldier*days worth of food consumption that 32 tons of rice will give you.

 

Thus 1/R * 32 tons = 32 tons / R = 32 * 1080 soldier days =  34560 soldier days 

 

Then divide this number of soldier days by the number of solders (540)

 

Thus we have the equation

 

1/R * 32 tons / 540 days = 1080 (soldier * days / ton) * 32 tons / 540 soldiers

 

The units cancel, getting us 64 days. 

 

Answer 2

We start with 20 tonnes feeds 300 soldiers for 72 days

 

From this we can figure out how many tonnes of rice each soldier requires per day

 

(20 tonnes)/(300 soldiers) = 1/15 tonnes per soldier

 

dividing the 1/15 tonnes per soldier by 72 days gives

 

(1/15)/72 = 1/((15)(72)) = 1/1080 tonnes per soldier per day

 

We can use this to set up a proportion

 

1 is to 1080   as   32 tonnes is to 540 soldiers over x days 

or 1 is to 1080 as 32 is to 540x

 

1/1080 = 32/540x

 

cross multiply 540x = 1080(32)

 

x = 1080(32)/540 = 64 days