An army of 1500 men has provisions for 50 days. After 10 days, due to injuries…
2017
An army of 1500 men has provisions for 50 days. After 10 days, due to injuries some of them left, and the remaining food was now sufficient for the next 50 days for the remaining men. The number of men who left is:
- A.
300 men
- B.
310 men
- C.
200 men
- D.
250 men
Attempted by 5 students.
Show answer & explanation
Correct answer: A
Concept
In provision problems the total stock of food is measured in man-days: total man-days = (number of men) x (number of days). This quantity is fixed by how much food exists, so the food eaten in any period equals (men present) x (days elapsed), and the food still left equals the original total minus what has been consumed.
Application
Total food at the start = 1500 x 50 = 75000 man-days.
Food consumed in the first 10 days (all 1500 men present) = 1500 x 10 = 15000 man-days.
Food remaining after 10 days = 75000 - 15000 = 60000 man-days.
Let the number of men remaining be R. This remaining food must last the next 50 days, so R x 50 = 60000, giving R = 60000 / 50 = 1200 men.
Men who left = original men - remaining men = 1500 - 1200 = 300.
Cross-check
Verify the balance: 1200 remaining men over 50 days need 1200 x 50 = 60000 man-days, exactly the food left after the first 10 days. So 300 is the number of men who left.