If Zeba had been 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. Her actual age now is ___ years.

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Solution

The correct option is D $14$
Let the actual age of Zeba be $x$ yrs
Her age when the was 5 yr younger $= (x - 5)$ yrs
Now, by given condition,
Square of her age $= 11$ more than five times her actual age
$(x - 5)^{2} = 5 x + 11 \Rightarrow (x - 5)^{2} = 5 x + 11 \Rightarrow x^{2} + 25 - 10 x = 5 x + 11 \Rightarrow x^{2} - 15 x + 14 = 0 \Rightarrow x^{2} - 14 x - x + 14 = 0 [b y s p l i t t i n g t h e m i d d l e t e r m] \Rightarrow x (x - 14) - 1 (x - 14) = 0 \Rightarrow (x - 1) (x - 14) = 0 \Rightarrow x = 14$
[here, $x \neq 1$ because her age is $x - 5$ , So, $x - 5 = 1 - 5 = - 4$ i.e., age cannot be negative]
Hence, Zeba's age now is $14$ years.

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Take Sarita’s present age to be $y$ years.

(i) What will be her age $5$ years from now?

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(iv) Grandmother is $2$ years younger than grandfather. What is grandmother’s age?

(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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