Question

Food in camp lasts for $8$ men for $29$ weeks. How long would the food last for $10$ men?
A. $22.3$ weeks
B. $24$ weeks
C. $32$ weeks
D. $23.2$ weeks

Answer 1

Hint: Here, we have to find the number of weeks that the food will last for $10$ men if for $8$ men the food lasts for $29$ weeks. So, firstly we will find the number of weeks that lasts for $1$ men and then we will divide the number of weeks that lasts for $1$ men by $10$ in order to find the number of weeks for $10$ men. So basically, we will use the concept of the unitary method.

Complete step by step answer:
In Mathematics Unitary Method is a fundamental concept which helps us to solve various sums and this method generally involves finding the value of a unit in the given terms, using which the value of the given quantity of units can be calculated. According to the question, food in camp lasts for $8$ men for $29$ weeks and we have to calculate the food last for $10$ men. Given that number of weeks food lasts for $8$ men $ = 29$ weeks.
Now, the number of weeks food lasts for $1$ men $ = 29 \times 8$ weeks.
$ \Rightarrow 29 \times 8 = 232$ weeks
Therefore, the number of weeks food lasts for $10$ men $ = \dfrac{{232}}{{10}}$ weeks
$ \therefore \dfrac{{232}}{{10}} = 23.2$

Hence, option D is the correct answer.

Note: In order to solve these types of problems first we have to recognize the unknown and known values. The concept of the unitary method is also linked to ratio and proportion. If we have to find the ratio of one quantity for another we require the concept of unitary method. There are two types of unitary method depending upon the value and quantity of a unit to be calculated they are Direct Variation and Indirect variation. In direct variation there is an increase or decrease in one quantity and this reflects on the increase or decrease in other quantities whereas the inverse of direct variation results in inverse variation that means one increase results in the decrease of the other quantity.