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?



In this math problem solving we have ,


Food Provision is sufficient for ;

=6weeks=6\times 7= 42days

Men left after two  weeks;


Men left in the camp after four weeks;


So we are left with days;

4weeks= 4 \times7= 28 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’;


\Rightarrow x=\frac{1500\times 28}{1050}=40 days

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


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’;
\Rightarrow 40\left ( Y+500 \right )=50y
\Rightarrow 40Y+20000 =50Y
\Rightarrow 50Y-40Y=20000
\Rightarrow Y =\frac{20000}{10}\Rightarrow Y=2000
So, there were 2000 men at the start.



You may submit a MCQ or maths problem with solution tips here in the comment box below! If you could not solve anyone, you may submit a MCQ or maths problem without solution as well. We will try our level best to solve it for you!

Your email address will not be published.

You may use these <abbr title="HyperText Markup Language">HTML</abbr> tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>