Question

If zeba were younger by 5 years then what she really is then the square of her age is 11 more than 5 times her real age. Find her actual age

Answer 1

Answer:

Zeba�s present age is 14 years.

Step-by-step explanation:

Let the present age of Zeba is x years.

Then, 5 years before her age would be (x � 5) years

According to the question, (x � 5)2 = 11 + 5x  

x2 + 25 -10x = 11 + 5x

x2 � 15x + 14 = 0    

x2 � 14x - x + 14 = 0

x(x � 14)-1(x-14)=0

(x-1)(x-14) = 0

x =1 or 14  

x =1 is rejected since in this case before 5 years her age would be negative which is not possible.      

So, Zeba�s present age is 14 years.

Answer 2

Let the present age of Zeba = x years

5 years ago:

$\longrightarrow$$\sf{ {(x - 5)}^{2} = 5x + 11}$

$\longrightarrow$$\sf{ {x}^{2} - 10 + 25 = 5x + 11}$

$\longrightarrow$$\sf{ {x}^{2} - 15x + 14 = 0}$

$\longrightarrow$$\sf{(x - 1)(x - 14) = 0}$

$\longrightarrow$$\sf{x = 1 \: or \: x = 14}$

But x ≠ 1, because then x - 5 would be negative.

Hence, the present age of Zeba = 14 years.