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In a garrison of 3600 men, the provisions were sufficient for 20 days at the rate of 1.5 kg per man per day. If x more men joined, the provisions would be sufficient for 12 days at the rate of 2 kg per man per day. Find x.
- a)600
- b)800
- c)900
- d)720
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a garrison of 3600 men, the provisions were sufficient for 20 days ...
Let x be the number of new men joined the garrison,
The total quantity of food is = 3600(20) (1.5) kg ----------1
Now the available food will be consumed by (3600+x) men
(3600+x) (12) (2) kg --------------2
1 = 2
Solving both the equations
3600(20) (1.5) = (3600+x) (12) (2)
108000 = 86400 + 24x
21600 = 24x
X = 900
900 more men joined the garrison.
The total quantity of food is = 3600(20) (1.5) kg ----------1
Now the available food will be consumed by (3600+x) men
(3600+x) (12) (2) kg --------------2
1 = 2
Solving both the equations
3600(20) (1.5) = (3600+x) (12) (2)
108000 = 86400 + 24x
21600 = 24x
X = 900
900 more men joined the garrison.
Most Upvoted Answer
In a garrison of 3600 men, the provisions were sufficient for 20 days ...
Given:
- A garrison of 3600 men
- Provisions sufficient for 20 days at the rate of 1.5 kg per man per day
- If x more men joined, the provisions would be sufficient for 12 days at the rate of 2 kg per man per day
To find: x (number of men who joined)
Assumptions:
- The amount of provisions required per day per person is constant
- The total amount of provisions required is directly proportional to the number of men in the garrison
Solution:
Let the initial amount of provisions be P kg.
Amount of provisions required per day for 3600 men at the rate of 1.5 kg per man per day:
= 3600 x 1.5 = 5400 kg/day
Total amount of provisions required for 20 days:
= 5400 x 20 = 108000 kg
Amount of provisions required per day for (3600 + x) men at the rate of 2 kg per man per day:
= (3600 + x) x 2 = 7200 + 2x kg/day
Total amount of provisions required for 12 days:
= (7200 + 2x) x 12 = 86400 + 24x kg
Since the amount of provisions is constant in both cases, we can equate them:
108000 = 86400 + 24x
21600 = 24x
x = 900
Therefore, the number of men who joined is 900.
Answer: Option (c) 900
- A garrison of 3600 men
- Provisions sufficient for 20 days at the rate of 1.5 kg per man per day
- If x more men joined, the provisions would be sufficient for 12 days at the rate of 2 kg per man per day
To find: x (number of men who joined)
Assumptions:
- The amount of provisions required per day per person is constant
- The total amount of provisions required is directly proportional to the number of men in the garrison
Solution:
Let the initial amount of provisions be P kg.
Amount of provisions required per day for 3600 men at the rate of 1.5 kg per man per day:
= 3600 x 1.5 = 5400 kg/day
Total amount of provisions required for 20 days:
= 5400 x 20 = 108000 kg
Amount of provisions required per day for (3600 + x) men at the rate of 2 kg per man per day:
= (3600 + x) x 2 = 7200 + 2x kg/day
Total amount of provisions required for 12 days:
= (7200 + 2x) x 12 = 86400 + 24x kg
Since the amount of provisions is constant in both cases, we can equate them:
108000 = 86400 + 24x
21600 = 24x
x = 900
Therefore, the number of men who joined is 900.
Answer: Option (c) 900
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