Akash has $8 x y + 4 x y^{2}$ chocolates. He wants to distribute them to $2 x$ children. How many chocolates does each of the child get if $y = 2$ ?

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Solution

The correct option is B 16
$2 x$ children will get $8 x y + 4 x y^{2}$ chocolates.
So, 1 child will get $\frac{8 x y + 4 x (y^{2})}{2 x}$ chocolates.
Factorize $8 x y + 4 x y^{2}$ by using method of common factors.
$2 \times 2 \times 2 \times x \times y + 2 \times 2 \times x \times y \times y = 2 x (3 y + 2 y^{2})$
So, $\frac{8 x y + 4 x (y^{2})}{2 x}$
= $\frac{2 x (4 y + 2 y^{2})}{2 x}$
= $(4 y + 2 y^{2})$
Given, $y = 2$ .
So, substituting the value of $y$ in $(4 y + 2 y^{2})$ we get,
⇒ $4 \times 2 + 2 \times 2 \times 2$
$= 8 + 8$
$= 16$

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