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A Garrison of 500 Men had Provisions for 27 Days. After 3 Days a Reinforcement of 300 Men Arrived. For How Many More Days will the Remaining Food Last Now?

  • A garrison of 500 men had provisions for 27 days.
  • After 3 days a reinforcement of 300 men arrived.
  • Total days the remaining food would last can be figure out in this way.

Explanation

Two given entities here are

  • Men
  • Days

To determine the relation here, let suppose; total days the remaining food would last = y

Case

500 men had provisions for 24 days.

After 3 days a reinforcement of 300 men arrived so total men = 500 + 300 = 800 men

Men           Days

 500              24

 800              y

  • Less men mean more days.
  • More men mean less days.

This clearly indicates that there is inverse relation.

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

500 : 800  ::  y : 24 ________ (i)

800 x y = 500 x 24 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 15 days).

To Find

Total days the remaining food would last = ?

Solution

Method I

Let suppose

Total days the remaining food would last = y

Men           Days

 500              24

 800              y

  • Relation between men and days is inverse.

So

500 : 800  ::  y : 24

800 x y = 500 x 24

800 x y = 12000

800y = 12000

y = 12000/800

y  = 120/8

y = 15

Total days the remaining food would last = 15 days

Method II

Total provisions = 500 x 27

Total provisions = 13500

3 days provisions = 500 x 3

3 days provisions = 1500

Remaining provisions = 13500 – 1500

Remaining provisions = 12000

After 3 days 300 men join the camp

Total men = 500 + 300

Remaining men = 800 men

Total days the food would last = 12000/800

Total days the food would last = 15 days

Total days the food would last = 15 days

Conclusion

A garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. The remaining food would last for 15 days.

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