A Garrison of 120 men has a provision of 30 days. At then end of 5 days,5 more men joined them. How many days can they sustain on remaining provision.
Inverse Variation: Garrison of 120 Men has a provision for 30 days.
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0Suppose one man needs 37 units of provision each day. How much provision is there at the start? How much is still there after 5 days? How long will that much last with 5 more men around? – 2012-05-07
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2Inverse Variation? Anyway, just imagine that every man requires exactly one banana a day. Now it's easy: (i) How many bananas did they start with? (ii) How many bananas are left after five days? (iii) How many days will these remaining bananas feed 125 men for? – 2012-05-07
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1@Gerry: I take it your unit of provision is 1/37th of a banana? – 2012-05-07
1 Answers
More or less, as TonyK indicated in a comment:
If you have enough provisions for 120 men for 30 days, then you have how many man-days of provisions? That is, how many days would the given provisions last with 1 man or how many men could the given provisions support for just 1 day?
$120\text{ men}\cdot30\text{ days}=3600\text{ man}\cdot\text{days}$
Now, how many man-days of provisions are consumed after 5 days with 120 men? How many man-days of provisions are left?
$120\text{ men}\cdot5\text{ days}=600\text{ man}\cdot\text{days}$ of provisions used; $3600\text{ man}\cdot\text{days}-600\text{ man}\cdot\text{days}=3000\text{ man}\cdot\text{days}$ of provisions left
Finally, with 5 more men, there are $120+5=125$ men, so how many days will the remaining provisions last?
$$\frac{3000\text{ man}\cdot\text{days}}{125\text{ men}}=\frac{3000}{125}\text{ days}=\cdots$$