Raghu's father gave him $₹ (3 x y + x^{2})$ and his brother gave him $₹ 3 (2 x^{2} + 5 x y)$ , out of this he spent $₹ (x^{2} + 2 x y)$ on cricket kits, $₹ (x^{2} + x y)$ on clothes . If x = 2 and y = 3, then find the total amount left with him.

₹185

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₹110

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₹275

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₹268

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Solution

The correct option is B ₹110
The total amount received by Raghu is
$= ₹ (3 x y + x^{2})$ + $₹ 3 (2 x^{2} + 5 x y)$
$= (7 x^{2} + 18 x y)$ .
Total amount Raghu spent
$= ₹ ((x^{2} + 2 x y) + (x^{2} + x y)$
$= ₹ (2 x^{2} + 3 x y)$
Amount of money left
$= ₹ (7 x^{2} + 18 x y)$ - $(2 x^{2} + 3 x y)$ ,
$= ₹ (5 x^{2} + 15 x y)$ .
Substituting the value of $x = 2$ and $y = 3$ in the above expression, we get,
$₹ [5 (2)^{2} + 15 (2) (3)]$
= ₹110
Hence, the amount of money left with Raghu is ₹110.

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