Question

the product of the ages of sohail and nikhil is 360. if twice the age of nikhil is more than sohail's age by 6 years, what is nikhil's age?

Answer 1

Let Nikhil's age be x years
then,Sohail's age will be 360/x
now,A/Q
2x=(360/x)+6
$2x = (360 \div x) + 6 \\ or \: 2x = (360 + 6x) \div x \\ or2 {x}^{2} = 360 + 6x \\ or {x}^{2} = (360 + 6x) \div 2 \\ or {x}^{2} = 180 + 3x \\ or {x}^{2} - 3x - 180 = 0 \\ now \:solving \: it \: using \: quadratic \: \\ equation \: formula \\ we \: get \\ (3 + - \sqrt{729} ) \div 2 \\ (3 + 27) \div 2 \\ 30 \div 2 \\ 15 \\ or \\ (3 - 27) \div 2 = \\ - 24 \div 2 \\ = - 12$
since x is the value of age hence
x=15
so Nikhil's age =15 years
Sohail's age = 360/15= 24 years.

Answer 2

Let Nikhil's age be x years

then,Sohail's age will be 360/x

now,A/Q

2x=(360/x)+6

$\begin{lgathered}2x = (360 \div x) + 6 \\ or \: 2x = (360 + 6x) \div x \\ or2 {x}^{2} = 360 + 6x \\ or {x}^{2} = (360 + 6x) \div 2 \\ or {x}^{2} = 180 + 3x \\ or {x}^{2} - 3x - 180 = 0 \\ now \:solving \: it \: using \: quadratic \: \\ equation \: formula \\ we \: get \\ (3 + - \sqrt{729} ) \div 2 \\ (3 + 27) \div 2 \\ 30 \div 2 \\ 15 \\ or \\ (3 - 27) \div 2 = \\ - 24 \div 2 \\ = - 12\end{lgathered}$