Question

Family of 4 members consumes $6{\rm{ kg}}$ of sugar in a month. What will be the monthly consumption sugar, if the number of family members becomes $6?$

Answer 1

Hint:Here we are going to use the unitary method to solve this problem, that is we are going to find the weight of sugar consumed by one person. With the help of the found weight we multiply the number of persons whose sugar consumption is to be found which will lead us to the required answer.

Complete step-by-step answer:
Unitary method: The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

Now we have the quantity of sugar consumed by \[4\] members of a family.
That is, it is given that \[6{\rm{ kg}}\] of sugar is consumed by 4 members.
By the unitary method first we have to find quantity of single unit value
Therefore, now we are going to find the sugar consumed by a single member in a family. By dividing the quantity of sugar \[6{\rm{ kg}}\] by the number of members in a family \[4\] members.
Hence,
\[ \Rightarrow {\rm{ }}\dfrac{6}{4} = \dfrac{3}{2}\]
\[ \Rightarrow {\rm{ }}\dfrac{3}{2} = 1.5\;{\rm{kg}}\]
Therefore a single member of the family consumes \[1.5\;{\rm{kg}}\] of sugar in a month.
Again using the unitary method we have to multiply the single unit value with our required value.
We have to find the quantity of sugar consumed by \[6\] members of a family in a month.
Hence we have to multiply the quantity of sugar consumed by a single person \[1.5\;{\rm{kg}}\] by \[6\]. Because we have to find the quantity of sugar for \[6\] members.
\[ \Rightarrow {\rm{ 1}}{\rm{.5}} \times {\rm{6}}\;{\rm{kg}}\]
\[ \Rightarrow {\rm{ 9}}\,{\rm{kg}}\]
Now we have found the quantity of sugar consumed by \[6\] members of the family as \[{\rm{9}}\,{\rm{kg}}\].
Hence, if the number of family members becomes \[6\] they consume \[{\rm{9}}\,{\rm{kg}}\] of sugar in a month.

Note: In the above problem we divided 6 by 4 initially because when we divide the amount consumed by the number of persons we get the amount consumed by a single person, which is nothing but the first step of the unitary method. While using a unitary method we should be careful in finding the value used by one person.