If Zeba were younger by $5$ years than what she really is, then the square of her age (in years) would have been $11$ more than five times her actual age. What is her age now?

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Solution

Let $x =$ Zeba age
As per question given the following equation can be formed:
$\Rightarrow (x - 5)^{2} = 11 + 5 x$
$\Rightarrow x^{2} - 10 x + 25 = 11 + 5 x$
$\Rightarrow x^{2} - 10 x + 25 - 11 - 5 x = 0$
$\Rightarrow x^{2} - 15 x + 14 = 0$

$\Rightarrow x^{2} - 14 x - x + 14 = 0$
$\Rightarrow x (x - 14) - 1 (x - 14) = 0$
$\Rightarrow (x - 14) (x - 1) = 0$
$x = 14$ or $x = 1$
Since her age can't be $1$ , So it is $14$

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(iii) Sarita’s grandfather is $6$ times her age. What is the age of her grandfather?

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(v) Sarita’s father’s age is $5$ years more than $3$ times Sarita’s age. What is her father’s age?

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If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?

Let x= Zeba ageAs per question given the following equation can be formed:⇒(x−5)2=11+5x⇒x2−10x+25=11+5x⇒x2−10x+25−11−5x=0⇒x2−15x+14=0⇒x2−14x−x+14=0⇒x(x−14)−1(x−14)=0⇒(x−14)(x−1)=0x=14 or x=1Since her age can't be 1, So it is 14

If Zeba were younger by $5$ years than what she really is, then the square of her age (in years) would have been $11$ more than five times her actual age. What is her age now?