- 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.
