### Brain Teasers

# Food Scarcity

A garrison of 3300 men had provisions for 32 days, when given at the rate of 850 gms. per head. At the end of 7 days, a reinforcement arrives and it is found that the provisions will last 17 days more, when given at the rate of 825 gms. per head.

What is the strength of the reinforcement?

What is the strength of the reinforcement?

### Answer

Strength of reinforcement = 1700. Hence total men = 5000.The key equation is:

(# of men) x (food per man) * (# of days) = (food consumed in the given time)

First figure out the initial amount of food:

3300 men x 850 g/man x 32 days = 89760000 grams

Food used after 7 days:

3300 men x 850 g/man x 7 days = 1963500 grams

Food remaining after 7 days:

89760000 - 1963500 = 70125000 grams

Now you know everything but the number of men present for the last 17 days. Just use the same equation to figure it out:

(# of men) x 825 g/man x 17 days = 70125000 grams

Solve for the number of men to get 5000. This means that 5000 - 3300 = 1700 men were provided with the reinforcement.

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