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If Zeba were younger by 5 years than wha...

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?

Text Solution

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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.
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