d math problem solving A fort is provisioned for 75 days

# Word Problem 4 & 5

Problem 4: A garrison of 1500 men has provision for 6 weeks. At the end of two weeks, 450 men leave. How long after this will the food last?

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Solution:

In this math problem solving we have ,

Food Provision is sufficient for ;

Men left after two  weeks;

Men left in the camp after four weeks;

;

So we are left with days;

Now data  can be arranged in a way;

i-e if the number of men decreases, for more days will be the food sufficient! So, this is a problem of inverse proportion;

solve for ‘x’;

So, the provision will go for 40 days onward.

Problem 5: A fort is provisioned for 75 days. After 25 days a reinforcement of 500 men arrives and the food then lasts only for 40 days. How many men were there in the fort ?

a)  2000                      b) 1000                      c) 1500                 d)  none

Solution:

In this math problem solving we suppose in the beginning that there were ‘y’ men. So, after 25 days, after arrival of 500 men, there will be total men ‘y+500’, and days left will be 50 . We arrange this data systematically as below;

This is inverse proportion problem, i-e if number of men increases, then food will last for less number of days !
Solving for ‘y’;
So, there were 2000 men at the start.