Thrice the square of a natural number decreased by four times the number is equal to 50 more than the number, the number is -

Answer: Option B

Let the number be x
According to question
$$\begin{array}{rl}& \left(3\times x^2\right)\text{ - }\left(4\times x\right)=50+x.....(i)\\ & \Rightarrow 3x^2-4x=50+x\\ & \Rightarrow 3x^2-5x-50=0\\ & \Rightarrow 3x^2-15x+10x-50=0\\ & \Rightarrow 3x^{}(x-5)+10(x-5)=0\\ & \Rightarrow (x-5)(3x+10)=0\\ & x=5or-\frac{10}{3}\end{array}$$
Since the natural number is x = 5

Shortcut method :
$$\Rightarrow 3x^2-4x=50+x.....(i)$$
Now put the value of x from option (b)
$$\begin{array}{rl}& x=5\\ & 3\times (5{)}^2-4\times 5=50+5\\ & 75-20=55\\ & 55=55\end{array}$$
LHS = RHS (it satisfies the conditions)
$$\text{so, x = 5}$$