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 iss
Answers
Answer:
420
Step-by-step explanation:
Let the food consumed by 1 man in 1 day be "manday"
The food provision is for 2100 men for 50 days.
=> The food is worth 2100*50 mandays
=> The food is worth 105000 mandays
After 10 days, some men left.
During the ten days, the food was consumed by 2100 men.
The food consumed was worth 2100*10 mandays
The food consumed was worth 21000 mandays
=> After 10 days, the food stock remaining was 105000 - 21000 mandays
=> After 10 days, the food stock remaining was worth 84000 mandays ..(i)
Let the number of men leaving = x
=> The number of men remaining = 2100 - x
We are given that the remaining food stock lasted for 50 days.
The food consumed by the remaining (2100 - x) men for 50 days
= 50(2100 - x)
From (i), we know that the food stock remaining was for 84000 mandays
=> 50(2100 - x) = 84000
=> 105000 - 50x = 84000
=> 50x = 21000
=> x = 420
The number of men leaving = 420
Verification:
Full provision of food = 2100*50 = 105000 mandays
For ten days, 2100 consumed food. This food was worth 21000 mandays
Food remaining = 84000 mandays ...(a)
After 10 days, 420 people left
People remaining = 1680
These 1680 people consumed food for 50 days.
The food consumed = 1680*50 = 84000 mandays ...(b)
Verified from (a) and (b)