Question

A garrison of $'n'$men had enough food to last for 30 days. After 10 days, 50 more men joined them. If the food now lasted for 16 days; what is the value of $n$?
(A) 200
(B)240
(C) 280
(D) 320

Answer 1

Hint:-Here, at first we have to find the relation between food consumed and the number of men for a given period or number of days. Then, we have to form a linear equation using the information provided in the problem. Now solving the equation, the value of $'n'$can easily be obtained.

Complete step-by-step answer:
Given, a garrison of $'n'$ men had enough food to last for 30 days.
In this problem, the value $'n'$ is to be known.
Thus, the variable is $'n'$
Now, after 10 days, 50 more men joined them. This means, the food has been consumed for 10 days and the food that is left will remain for the next 20 days if the same number of men are there.
Now, the remaining food lasted for 16 days.
Thus, the food for a garrison of $'n'$ men for the next 20 days should be equal to the food for (n+50) men for 16 days.
[$\therefore $50 men joined after 10 days,
$\therefore $ No. of men $ = n + 50$].
According to the problem,
$20 \times n = \left( {n + 50} \right) \times 16.$
$ \Rightarrow 20n = 16n + 800$
Now, a variable should be kept in one side, to obtain its value
$\therefore \;\;20n - 16n = 800$
$ \Rightarrow 4n = 800$
$ \Rightarrow n = \dfrac{{800}}{4} = 200$
$\therefore $ The value of n is 200.
The correct option is (A).

Note: In this type of problem, Firstly all the information given in the question should be gathered properly. Then with the help of that information, the equation should be formed. The steps involved in this type of problem –
(1) From the linear equation in one variable using the conditions given in the problem.
(2) Solve the equation for the unknown [by putting the variable in only one side of the equation] and then get the result.