Question

in a group of children each child gives a gift to every child if the total no. of gift is 132 find the no. of children ​

Answer 1

no of childrens 12 then each children gives a gift to 11 children

so that 12 multiply by 11 = 132 total no of gifts

Answer 2

$\underline\mathfrak{Given:-}$

• A group of children each child gives a gift to every child if the total no. of gift is 132

$\underline\mathfrak{To \: \: Find:-}$

• find the no. of children ......?

$\underline\mathfrak{Solutions:-}$

Let number of children be x.

And each child gives a gift to every other child.

so, one child gives x - 1 gifts to others.

$\: \: \: \: \: \therefore \: \: {x} \: {(x \: - \: {1})} \: \: = \: \: {132}$

$\: \: \: \: \: \leadsto \: \: {x}^{2} \: - \: {x} \: - \: {132} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {x}^{2} \: - \: {12x} \: + \: {11x} \: - \: {132} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {x} \: {({x} \: - \: {12})} \: + \: {11} \: {({x} \: - \: {12})} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {({x} \: - \: {12})} \: \: \: {({x} \: + \: {11})}$

$\: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {-11} \: \: \: and \: \: \: {x} \: \: = \: \: {12}$

Hence, the number of children is 12.