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?

Options

A. 13 Yrs
B. 14 Yrs
C. 15 Yrs
D. 16 Yrs

Answer

B

Explanation

Let the actual age of Zeba `=x` yr.
Herage when she was 5 yr younger `=(x-5)yr`.
Now by given condition
Square of her `=11` more than five times her actual age
`(x-5)^(2)=5xx` actual age `+11`
`implies(x-5)^(2)=5x+11`
`implies x^(2)+25-10x=5x+11`
`implies x^(2)-15x-14=0`
`implies x^(2)-14x-x+14=0` [by splitting the middle term]
`implies x(x-14)-1(x-14)=0`
`implies (x-1)(x-14)=0`
`x=14`
[here `x!=1` because her age is `x-5`. So `x-5=1-5=-4` i.e. age cannot be negative]
Hence required Zeba's age now is 14 yr.