Question

405 toffees distributed equally among children in such a way that the number of toffees received by each child is \[20\% \] of the total number of children. How many toffees did each child get?

Answer 1

Hint: Assume any variable for the total number of children then try to find it by formulating an equation using the property given for the number of children and by the result we can get using a unitary method.
Complete step by step answer:
Let us assume that there are total x number of children and as 405 toffees are equally distributed then by unitary method we can say that each children will receive only \[\dfrac{{405}}{x}\] number of toffees i.e., total number of toffees divided by total number of children and now coming to the second case it is given that \[20\% \] of total number of children is the number of toffees received by each number of children and that will be
\[\begin{array}{l}
20\% \text{of} (x)\\
 = x \times \dfrac{{20}}{{100}}\\
 = x \times \dfrac{1}{5}\\
 = \dfrac{x}{5}
\end{array}\]
It is very much clear that both of these are the total number of toffees received by each child so we can equate them. That will give us
\[\begin{array}{l}
\dfrac{x}{5} = \dfrac{{405}}{x}\\
 \Rightarrow {x^2} = 405 \times 5\\
 \Rightarrow {x^2} = 81 \times 5 \times 5\\
 \Rightarrow {x^2} = 9 \times 9 \times 5 \times 5\\
 \Rightarrow x = \sqrt {9 \times 9 \times 5 \times 5} \\
 \Rightarrow x = 9 \times 5
\end{array}\]
Now as we have the value of x let us put it in \[\dfrac{x}{5}\] to get the total number of toffees each child got an that will be
\[\dfrac{x}{5} = \dfrac{{9 \times 5}}{5} = 9\]
That means that each child got 9 toffees.

Note: I have not multiplied \[x = 9 \times 5\] because i knew that 5 will eventually get cancelled and although the value of x is not what we were told to find so we can leave it like that. Thus, It helps us in further calculations.