Question

A garrison of 750 men has provisions for 20 weeks. If at the end of 4 weeks, the garrison is reinforced by 450 men, for how many more weeks will the provisions last now?

• A. 9weeks
• B. 10weeks
• C. 6weeks
• D. 15weeks
• E. None of these

Answer 1

The Correct Option is A

Step 1: Understand the problem.
Initially, there are 750 men in the garrison, and the provisions are enough to last for 20 weeks. After 4 weeks, 450 more men are added to the garrison. We need to calculate for how many more weeks the provisions will last after the reinforcement.

Step 2: Calculate the total provisions available in man-weeks.
The total provisions available are enough to last for 20 weeks for 750 men. The total provisions in terms of man-weeks are:
Total provisions = \( 750 \times 20 = 15000 \) man-weeks.

Step 3: Calculate the provisions consumed in the first 4 weeks.
In the first 4 weeks, 750 men consume:
Provisions consumed = \( 750 \times 4 = 3000 \) man-weeks.
So, after 4 weeks, the remaining provisions are:
Remaining provisions = \( 15000 - 3000 = 12000 \) man-weeks.

Step 4: Calculate the new number of men after reinforcement.
After 4 weeks, 450 more men are added to the garrison, making the total number of men:
Total men = \( 750 + 450 = 1200 \) men.

Step 5: Calculate how many more weeks the remaining provisions will last.
The remaining provisions (12000 man-weeks) will now be used by 1200 men. The number of weeks the remaining provisions will last is:
Number of weeks = \( \frac{12000}{1200} = 10 \) weeks.
But we have already spent 4 weeks, so the provisions will last for \( 10 - 1 = 9 \) more weeks.

Step 6: Conclusion.
The provisions will last for 9 more weeks after the reinforcement.

Final Answer:
The correct option is (A): 9 weeks.