Question

a garrison is provided with rations for 80 soldiers for 60 days. find how long the rations will last if 20 more soldiers join them after 15 days

Answer 1

Answer:

A garrison is provided with ration for 80 soldiers to last 60 days. Find how long the

ration will last if 20 additional soldiers join them after 15 days.

Answer 2

Answer:

The total number of days the rations will last will be 36.

Step-by-step explanation:

Given that:

Total number of days = 60 days

So, after 15 days:

No of the days will be 60 - 15 = 45 days

Number of soldiers in the beginning = 80

The number of soldiers who joined later = 80 + 20

= 100

Let the number of days the rations will last be x

So, for 80 soldiers we have 45 days

Then, for 100 soldiers we have x

Now we will apply inverse proportion

∴ $\frac{80}{45}$ = $\frac{100}{x}$

80 × 45 = 100x

3600 = 100x

x = $\frac{3600}{100}$

x = 36 days

Hence, the total number of days the rations will last will be 36 days.

How does inverse proportion work?

When one number rises while the other falls, an inverse proportion is created. For instance, if there were more people working on a project, it would be finished faster. They have an inverse relationship. When one variable decline, the others also decline in the same ratio. When two variables move in opposite directions, one variable reduces as another increase and the other increases as another variable lowers, the variables are said to be inversely proportional. Direct proportion is in opposition to it. Inverse proportion is defined as y = k/x, where x and y are two numbers that are in inverse proportion, and k is the proportionality constant.

Thus, an elementary and suitable example of an inversely proportional relationship is the one between speed and time.