Correct answer is: b) 13

Explanation

The given equation is:
\large\frac{1}{2}\normalsize\left(x+1\right)+\large\frac{1}{3}\normalsize\left(x+2\right)+\large\frac{1}{4}\normalsize\left(x+3\right)=16
\rightarrow\large\frac{x+1}{2}+\large\frac{x+2}{3}+\large\frac{x+3}{4}\normalsize=16
\rightarrow\large\frac{6\left(x+1\right)+4\left(x+2\right)+3\left(x+3\right)}{12}\normalsize=16
\rightarrow 6x+6+4x+8+3x+9=16\times12
\rightarrow 13x+23=192
\rightarrow 13x=192-23
\rightarrow 13x=169
\rightarrow x=\large\frac{169}{13}
\rightarrow x=13
\therefore The root of the equation is 13
Ans: The root of the equation is 13.