Ruhi’s mother is $26$ years older than her. The product of their ages (in years) $3$ years from now will be $360.$ Form a Quadratic equation so as to find Ruhi’s age

x ² + 32 x + 273 = 0

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x ² + 32 x – 273 = 0

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x ² - 32 x +273 = 0

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x ² -32 x - 273=0

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Solution

The correct option is D: $x^{2} + 32 x - 273 = 0$
Let Ruhi’s age $= x$ , then mother’s age $= x + 26$
After three years, Ruhi's age $= (x + 3)$ and her mother's age $= (x + 26 + 3) = (x + 29)$

So after $3$ years, it is given that the product of their ages is equal to $360.$
$(x + 3) (x + 29) = 360$
$\Rightarrow x^{2} + 29 x + 3 x + 87 = 360$

$\Rightarrow x^{2} + 32 x - 273 = 0$

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Ruhi’s mother is 26 years older than her. The product of their ages (in years) 3 years from now will be 360. Form a Quadratic equation so as to find Ruhi’s age

The correct option is D: x2+32x–273=0Let Ruhi’s age =x, then mother’s age =x+26After three years, Ruhi's age =(x+3) and her mother's age =(x+26+3)=(x+29) So after 3 years, it is given that the product of their ages is equal to 360. (x+3)(x+29)=360⇒x2+29x+3x+87=360 ⇒x2+32x−273=0

Ruhi’s mother is $26$ years older than her. The product of their ages (in years) $3$ years from now will be $360.$ Form a Quadratic equation so as to find Ruhi’s age