Roshan's mother gave him $₹ (6 x y + 6 x)$ and his father gave him $₹ 6 (x y + 2 x + 2)$ for his birthday. If he spent $₹ 3 (x y + x + 1)$ on his birthday party and if $x = 1$ and $y = 2,$ then find the total amount left with him.

₹40

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₹42

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₹43

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₹45

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Solution

The correct option is B ₹42
Amount given by Roshan's mother = $₹ (6 x y + 6 x)$
Amount given by Roshan's father = $₹ 6 (x y + 2 x + 2)$
Total amount that was given to Roshan
= $₹ (6 x y + 6 x) + ₹ 6 (x y + 2 x + 2)$
= $₹ [(6 x y + 6 x y) + (6 x + 12 x) + 12]$
= $₹ (12 x y + 18 x + 12)$
Given that total amount Roshan spent = $₹ 3 (x y + x + 1)$

Amount of money left
= $₹ (12 x y + 18 x + 12) - ₹ 3 (x y + x + 1)$
= $₹ [(12 x y - 3 x y) + (18 x - 3 x) + (12 - 3)]$
= $₹ (9 x y + 15 x + 9)$
Substituting $x = 1$ and $y = 2$ in the above expression, we get 9(1)(2) + 15(1) + 9= 18 + 15 + 9 = 42.
Hence, the amount left with Roshan is ₹42.

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