PREVIOUSLY ASKED IN:
PSC Miscellaneous Prelims 2018
Answer
200 days
Explanation
Initially, there was a provision for 4000 men for 190 days. After 30 days pass, the remaining food would be sufficient for those 4000 men for another (190 - 30) = 160 days. However, 800 men left, bringing the remaining men down to (4000 - 800) = 3200. Using the formula (Men1 × Days1) = (Men2 × Days2): 4000 men × 160 days = 3200 men × X days X = (4000 × 160) / 3200 = 200 days. The food will last for 200 days.
Key Points
- > Use the concept of 'Man-Days': M1 × D1 = M2 × D2.
- > Recalculate the days after the given time has passed.
- > Remaining days for original men (D1) = 190 - 30 = 160 days.
- > New number of men (M2) = 4000 - 800 = 3200 men.
- > Equation: 4000 × 160 = 3200 × D2.
- > Solving gives D2 = 200 days.
Additional Information
Inverse Proportion in Provision Problems
| Number of Men | Number of Days | Relationship |
|---|---|---|
| 4000 | 160 | Initial Base |
| 1 | 4000 × 160 | Less men means food lasts longer (Inverse) |
| 3200 | (4000 × 160) / 3200 = 200 | More men means food finishes faster |
Memory Tips
- The M1D1 Rule: Always adjust the days first. If 30 days have passed, ignore them. You only care about the remaining food, which equals 4000 men × 160 days. Then divide this total food pool by the new number of men (3200).