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| A Ration Problem (Posted on 2006-12-20) |
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A ship sails with a supply of rations for 60 days at a daily allowance of 2.1 pounds of food per head. After sailing for 20 days, the ship encounters a storm in which five members of the crew are washed overboard .
The damages sustained by the ship add a 24 days delay to the trip; thus, each crew member’s allowance must be reduced to 1.5 pounds of food per head.
Find the original number of members of the crew.
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Submitted by K Sengupta
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Rating: 3.2500 (4 votes)
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Solution:
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Let x be the required number of members of the crew. Then, there were 60*2.1*x = 126x pounds of total rations.
After 20 days, remaining quantity of rations = 126x*2/3 = 84x.
Now, for the remaining (40+24) = 64 days; the total quantity of rations supplied to the remaining (x-5) men = 1.5*64*(x-5) = 96(x-5)pounds.
Hence, 84x = 96(x-5), giving:
x = 40.
Consequently, the required original number of members of the crew = 40.
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