Question

41 Rohan's mother is 26 years older than him. The product of their ages after 3 years
will be 360 years. Represented the above situation in the form of quadratic equation

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Answer 1

To Find:-

• Find the value of x.

Given:-

• Rohan's mother is 26 years older than him. The product of their ages after 3 years will be 360 years.

Solution:-

$\tt \: Rohan's \: \: mother \: \: is \: \: 26 \: \: years \: \: older \: \: than \: \: him \: .$

$\tt \: Let \: \: Rohan's \: \: age \: \: be \: \: " x "$

$\tt \: Rohan's \: \: mother \: \: age \: \: is " x + 26 "$

$\tt \: After \: \: 3 \: \: years \: \: their \: \: she \: \: will \: \: be$

$\tt \: Rohan's \: \: age = ( x + 3 )$

$\tt \: Rohan's \: \: mother \: \: age = ( x + 26 + 3 ) = ( x + 29 )$

$\tt \: The \: \: product \: \: of \: \: their \: \: ages \: \: after \: \: 3 \: \: years \: \: is \: \: 360 \: years.$

$\tt\implies \: ( x + 3 ) ( x + 29 ) = 360$

$\tt\implies \: { x }^{ 2 } + 29x + 3x + 87 = 360$

$\tt\implies \: { x }^{ 2 } + 32x - 273 = 0$

$\tt\implies \: { x }^{ 2 } + 39x - 7x - 273 = 0$

$\tt\implies \: x ( x + 39 ) - 7( x + 39 ) = 0$

$\tt\implies \: ( x + 39 ) ( x - 7 ) = 0$

$\tt\implies \: x = - 39 \: ; \: 7$

$\tt\implies \: x = 7$

$\tt \: Hence \: ,$

• $\tt \: Rohan's \: \: age = 7 \: years$

• $\tt \: Mother's \: \: age = x + 26 = 33 \: years$

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

Let Rohan's present age be 'x' years.

So, mother present age be 'x + 26' years.

After 3 years,

• Rohan age be 'x + 3' years

• Mother age be 'x + 29' years.

$\bigstar \: \: \red{ \rm \: According \: to \: statement }$

• The product of their ages after 3 years will be 360 years.

$\rm : \implies \:(x + 3)(x + 29) = 360$

$\rm : \implies \: {x}^{2} + 29x + 3x + 87 = 360$

$\boxed{ \purple{ \rm : \implies \: {x}^{2} + 32x - 273 = 0}}$

is the required expression.