Akash has $6 x y + 4 x y^{2}$ chocolates. He distributed these chocolates among $2 x$ children. How many chocolates will each child get, if $y = 2$ ?

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Solution

The correct option is D 14
$2 x$ children will get $6 x y + 4 x y^{2}$ chocolates.
Then, each child will get $\frac{6 x y + 4 x y^{2}}{2 x}$ chocolates.

We shall factorise the numerator, $6 x y + 4 x y^{2}$ , by using the method of common factors.
$6 x y + 4 x y^{2} = (2 \times 3 \times x \times y) + (2 \times 2 \times x \times y \times y) = 2 x (3 y + 2 y^{2})$

$∴ \frac{6 x y + 4 x y^{2}}{2 x} = \frac{2 x (3 y + 2 y^{2})}{2 x} = (3 y + 2 y^{2}$ )

Given y = 2.
Substituting the value of y in $(3 y + 2 y^{2}$ ), we get,
$(3 \times 2) + (2 \times 2 \times 2) = 6 + 8 = 14$

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