0
$\begingroup$

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.

  • 0
    Suppose 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
  • 2
    Inverse 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
  • 1
    @Gerry: I take it your unit of provision is 1/37th of a banana?2012-05-07

1 Answers 1

0

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?

$$\frac{3000\text{ man}\cdot\text{days}}{125\text{ men}}=\frac{3000}{125}\text{ days}=\cdots$$