Question

A garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?
A) 15
B) 16
C) $17\dfrac{1}{2}$
D) 18

Answer 1

Hint: Find the total amount of meal by the product of men initially and the number of days provision lasts, in the same way find the amount of meal utilized before new men arrive, and their difference will give the remaining meal.
The number of days this remaining meal will last is given by its division with the total men

Complete step-by-step answer:
It is given that for
Men = 500, Provision lasts = 27 days
Thus, total meal can be given as:
500 X 27 = 13500
Meals used before new men arrived (as new men arrived after 3 days => the meals were utilized for 3 days by 500 men) :
500 X 3 = 1500
Then the remaining meal is given as:
Total meal – utilized meal
= 13500 – 1500
= 12000
When 300 new men arrive, the total number of men are:
500 + 300 = 800
The number of days (n) food will last will
\[
  n{\text{ }} = {\text{ }}\dfrac{{remaining{\text{ }}meal}}{{men}} \\
  n = \dfrac{{12000}}{{800}} \\
 \]
n = 15
Therefore, in a garrison of 500 men if the provisions were for 27 days and after 3 days if a reinforcement of 300 men arrived for 15 more days the remaining food would last.

Note: For the countable nouns like number of days, remember that these can’t be negative or in decimal or in mixed fraction and hence option C) gets cancelled already.