An army of 2100 men has provision for 50 days. After 10 days due to injuries…
2017
An army of 2100 men has provision for 50 days. After 10 days due to injuries some of them left and the food were now enough for next 50 days for remaining men. The number of men left is:
- A.
400
- B.
420
- C.
410
- D.
650
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
In any provisions/work problem the total resource is conserved and equals the product men × days, measured in man-days. The same stock of food gives a fixed number of man-days; if the number of men changes, the days it lasts adjust so that men × days stays equal to the food that remains.
Application
Total food provisioned at the start = 2100 × 50 = 105000 man-days.
Food consumed in the first 10 days by all 2100 men = 2100 × 10 = 21000 man-days.
Food still remaining after 10 days = 105000 − 21000 = 84000 man-days.
Let the number of men remaining be R. This remaining food must last 50 more days: R × 50 = 84000.
Solve for R: R = 84000 ÷ 50 = 1680 men remaining.
Men who left = original men − remaining men = 2100 − 1680 = 420.
Cross-check
Put R = 1680 back in: 1680 men for 50 days need 1680 × 50 = 84000 man-days, which is exactly the food left after 10 days. The balance holds, so 420 men left.