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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.