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A Fort had Provision of Food for 150 Men for 45 Days. After 10 Days, 25 Men Left the Fort. The Number of Days for which the Remaining Food will Last is?

  • A fort had provision of food for 150 men for 45 days.
  • After 10 days, 25 men left the fort.
  • The number of days for which the remaining food will last can be figure out in this way.

Explanation

Two given entities here are

  1. Men
  2. Days

To determine the relation here, let suppose; Number of days for which the remaining food will last = y

Case

As we know that;

Men           Days

150             35

125             y

  • Provision of food for days decreases as men increases.
  • Provision of food for days increases as men decreases.

This clearly indicates that there is inverse relation.

Direct/Indirect relation tells how the equation will be written.

150 : 125  ::  y : 35 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 42)

To Find

Number of days for which the remaining food will last = ?

Solution

Method I

Let suppose

Number of days for which the remaining food will last = y

Men           Days

150             35

125             y

Relation between men and days is inverse, so;

150 : 125  ::  y : 35

150 x 35 = y x 125

5250 = 125y

5250/125 = y

y = 42

Number of days for which the remaining food will last = 42 days answer

Method II

150 men had provision of food = 35 days

1 man had provision of food = 35 x 150 days

1 man had provision of food = 5250 days

125 man had provision of food = 5250/125 days

125 man had provision of food = 42 days

Number of days for which the remaining food will last = 42 days answer

Conclusion

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The remaining food will last for 42 days.

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