Given,

$1\frac{4}{7}+7\frac{1}{3}+3\frac{3}{5}=?$

It can be approximated as

$$\begin{gathered} 1\frac{4}{7}+7\frac{1}{3}+3\frac{3}{5}=? \\ =(1+7+3)+(\frac{4}{7}+\frac{1}{3}+\frac{3}{5}) \\ =\left(11\right)+\left(\frac{60+35+3}{105}\right) \\ = 11+\left(\frac{158}{105}\right) \end{gathered}$$

= 11+1.5

= 12.5 ≈ 13

Hence, Option D is correct.