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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?

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15

years

14

years

41

years

16

years

answer is B.

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Detailed Solution

It is given that 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.
Let x be the age of Zeba.
According to the given condition,

x − 5 2 = 11 + 5 x ⇒ x 2 + 25 − 10 x = 11 + 5 x ⇒ x 2 + 25 − 11 − 10 x − 5 x = 0 ⇒ x 2 − 15 x + 14 = 0

On factoring it, we get,

⇒ x 2 − 15 x + 14 = 0 ⇒ x 2 − 14 x − x + 14 = 0 ⇒ x x − 14 − 1 x − 14 = 0 ⇒ x − 1 x − 14 = 0 ⇒ x = 1, 14

The age cannot be

1

as the age before

5

years will make no sense.
So,

x = 1

is neglected.
Thus, the age of Zeba is

14

years.
Hence, the correct option is 2.

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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?

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