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01 Dec 2021, 03:45
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Difficulty:
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Question Stats:
72% (02:33) correct
28%
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wrong
based on 138
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In a garrison there are 600 soldiers and food supply they have is sufficient for 30 days. After 10 days, 200 more soldiers join. If rate of food consumption is same for every soldier, then how long will the food supply last after these 200 soldiers joined ?
A. 14 days
B. 15 days
C. 16 days
D. 21 days
E. 32 days
A. 14 days
B. 15 days
C. 16 days
D. 21 days
E. 32 days
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01 Dec 2021, 04:35
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Normal method:
S'pose one soldier eats 1kg per day, so 600 soldiers would eat 600*30*1 = 18000 kgs in 30 days.
That is 600 kgs per 600 soldiers per day. 200 more soldiers join after 10 days, so ration consumed in these 10 days = 600*10 = 6000 kgs.
Remaining ration = 18000 - 6000 = 12000kgs.
If no one joined, this 12000 kgs would have been consumed by 600 soldiers in 20 days (1kg/soldier).
But, the total no. of soldiers now = 800.
So, 12000 kgs of ration will now be consumed by 800 soldiers in 12000/800 = 15 days.
So, the ratio will now last for 15 days instead of 20.
Faster method:
Let the rate of consumption for each soldier be 1 kg/day.
Total ration = 600*30*1 = 18000 kgs. This is a Work-Rate equation. 600 soldiers with rate of consumption of 1 kg/day take 30 days to consume 18000 kgs.
In 10, 600 soldiers at a rate of consumption 1 kg/day would consume = 600*10*1 = 6000 kgs of ration.
So, 800 soldiers with the same rate of consumption of 1 kg/day will take \(x\) days to consume the remaining 12000 kgs of ration.
800*1*\(x\) = 12000.
\(x\) = 15 days.
S'pose one soldier eats 1kg per day, so 600 soldiers would eat 600*30*1 = 18000 kgs in 30 days.
That is 600 kgs per 600 soldiers per day. 200 more soldiers join after 10 days, so ration consumed in these 10 days = 600*10 = 6000 kgs.
Remaining ration = 18000 - 6000 = 12000kgs.
If no one joined, this 12000 kgs would have been consumed by 600 soldiers in 20 days (1kg/soldier).
But, the total no. of soldiers now = 800.
So, 12000 kgs of ration will now be consumed by 800 soldiers in 12000/800 = 15 days.
So, the ratio will now last for 15 days instead of 20.
Faster method:
Let the rate of consumption for each soldier be 1 kg/day.
Total ration = 600*30*1 = 18000 kgs. This is a Work-Rate equation. 600 soldiers with rate of consumption of 1 kg/day take 30 days to consume 18000 kgs.
In 10, 600 soldiers at a rate of consumption 1 kg/day would consume = 600*10*1 = 6000 kgs of ration.
So, 800 soldiers with the same rate of consumption of 1 kg/day will take \(x\) days to consume the remaining 12000 kgs of ration.
800*1*\(x\) = 12000.
\(x\) = 15 days.
27 May 2025, 19:29
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In a garrison there are 600 soldiers and food supply they have is sufficient for 30 days. After 10 days, 200 more soldiers join. If rate of food consumption is same for every soldier, then how long will the food supply last after these 200 soldiers joined ?
A. 14 days
B. 15 days
C. 16 days
D. 21 days
E. 32 days
Some one only thinking only about W = R*T would not be able to start with this problem
Work is a product of Rate, Time, No. of men, any other parameter
So, W = T*M -----> Time * No of men/employee/Machines/Soldiers
Soln:
W = T*M
Total Work (W) = 30 days * 600 soldiers = 18K
Now,
Work done by 600 soldiers in 10 days W' = 10*600 = 6K
Remaining Work,
18K - 6K = 12K
Since W = T*M ----> T = W/M
Time = 12k/800 (800 = 600 soldiers +200 soldiers that joined additionally)
Time = 15 days (B)
A. 14 days
B. 15 days
C. 16 days
D. 21 days
E. 32 days
Some one only thinking only about W = R*T would not be able to start with this problem
Work is a product of Rate, Time, No. of men, any other parameter
So, W = T*M -----> Time * No of men/employee/Machines/Soldiers
Soln:
W = T*M
Total Work (W) = 30 days * 600 soldiers = 18K
Now,
Work done by 600 soldiers in 10 days W' = 10*600 = 6K
Remaining Work,
18K - 6K = 12K
Since W = T*M ----> T = W/M
Time = 12k/800 (800 = 600 soldiers +200 soldiers that joined additionally)
Time = 15 days (B)
