d math problem solving A fort is provisioned for 75 days
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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?



 

Solution:

In this math problem solving we have ,

Men=1500

Food Provision is sufficient for ;

=6weeks=6\times 7= 42days

Men left after two  weeks;

=450

Men left in the camp after four weeks;

=1500-450=1050;

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’;

\frac{x}{28}=\frac{1500}{1050}

\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

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

 

 

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