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A garrison of 160 men has provision for 40 days. At the end of 10 days, 40 more men joined them. How many days could the soldiers sustain themselves if they had joined on the first day itself?
- a)20
- b)24
- c)32
- d)34
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A garrison of 160 men has provision for 40 days. At the end of 10 days...
160 men can last for 40 days
1 man can last for = 40 × 160 days
Total number of men = 160 + 40 = 200
200 soldiers can last for = (30 × 160/200) = 24 days
Most Upvoted Answer
A garrison of 160 men has provision for 40 days. At the end of 10 days...
Given Information:
- Initial number of men in the garrison = 160
- Provision available for 40 days
At the end of 10 days:
- 40 more men joined the garrison
To find:
- How many days can the soldiers sustain themselves if the 40 men had joined on the first day itself?
Let's solve the problem step by step:
Step 1: Calculate the total provision available for the initial 160 men.
- Total provision available = 160 men * 40 days = 6400 men-days
Step 2: Calculate the number of men after 10 days.
- Number of men after 10 days = 160 men + 40 men = 200 men
Step 3: Calculate the new provision available for the 200 men.
- New provision available = 200 men * x days
Step 4: Use the principle of proportionality to find the value of x.
- The provision available is inversely proportional to the number of men.
- Provision for 160 men * 40 days = Provision for 200 men * x days
- 6400 men-days = 200 men * x days
Step 5: Solve for x.
- x = (6400 men-days) / (200 men)
- x = 32 days
Therefore, if the 40 men had joined on the first day itself, the soldiers could sustain themselves for 32 days.
- Initial number of men in the garrison = 160
- Provision available for 40 days
At the end of 10 days:
- 40 more men joined the garrison
To find:
- How many days can the soldiers sustain themselves if the 40 men had joined on the first day itself?
Let's solve the problem step by step:
Step 1: Calculate the total provision available for the initial 160 men.
- Total provision available = 160 men * 40 days = 6400 men-days
Step 2: Calculate the number of men after 10 days.
- Number of men after 10 days = 160 men + 40 men = 200 men
Step 3: Calculate the new provision available for the 200 men.
- New provision available = 200 men * x days
Step 4: Use the principle of proportionality to find the value of x.
- The provision available is inversely proportional to the number of men.
- Provision for 160 men * 40 days = Provision for 200 men * x days
- 6400 men-days = 200 men * x days
Step 5: Solve for x.
- x = (6400 men-days) / (200 men)
- x = 32 days
Therefore, if the 40 men had joined on the first day itself, the soldiers could sustain themselves for 32 days.
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