A fort had provisions for 600 men for 180 days. After 10 days, 100 men left the fort. How long would the food last now at the same rate? Fabina borrows Rs.12500 at 12% p.a. for 3 y... A fort had provisions for 600 men for 180 days. After 10 days, 100 men left the fort. How long would the food last now at the same rate? Fabina borrows Rs.12500 at 12% p.a. for 3 years at simple interest and Radha borrows the same amount for the same period at 10% p.a. compounded annually. Calculate the simple interest paid by Fabina and the difference between SI paid by Fabina and CI paid by Radha. 'A' can do a piece of work in 20 days and 'B' can finish it in 30 days. They worked together for 10 days and then A left the work. B finished the remaining work. Find the total time taken to finish the whole work.
Understand the Problem
The question consists of three distinct mathematical problems involving provisions, simple interest, and work completion rates. It seeks to determine how long food would last in a fort after a certain change, calculate simple interest for a loan, and find the total time taken to complete a piece of work shared between two individuals.
Answer
The food would last for an additional $204$ days.
Answer for screen readers
The food would last for an additional ( 204 ) days.
Steps to Solve
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Calculate the total provisions initially available
The fort had provisions for 600 men for 180 days.
Total provisions = Number of men × Duration = $600 \times 180 = 108000$ man-days. -
Calculate provisions consumed in 10 days
In the first 10 days, there were 600 men consuming provisions.
Provisions consumed = $600 \times 10 = 6000$ man-days. -
Calculate remaining provisions after 10 days
Remaining provisions = Total provisions - Provisions consumed.
$$ \text{Remaining provisions} = 108000 - 6000 = 102000 \text{ man-days} $$ -
Calculate the new number of men after 10 days
After 10 days, 100 men left, so remaining men = $600 - 100 = 500$ men. -
Calculate how long remaining provisions will last for 500 men
Let $x$ be the number of days the remaining provisions last for 500 men.
$$ 500 \times x = 102000 $$ To find $x$, rearrange to:
$$ x = \frac{102000}{500} = 204 \text{ days} $$
The food would last for an additional ( 204 ) days.
More Information
This calculation demonstrates how resource management and consumption rates work together in determining the duration that supplies can last given changes in the number of consumers.
Tips
- Forgetting to account for the initial consumption before re-calculating the remaining provisions.
- Miscalculating the new number of men remaining after some have left.
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