If \(\frac{a}{3} = \frac{b}{4} = \frac{c}{7}\) then what would be the value of \(\frac{{a + b + c}}{a}\) ?

A \(4\frac{2}{3}\)

B \(2\frac{3}{4}\)

C \(1\frac{1}{3}\)

D \(\frac{{13}}{{17}}\)

E None of these

Correct Answer: Option A

Let \(\frac{a}{3} = \frac{b}{4} = \frac{c}{7} = p\)

\(\Rightarrow a = 3p,b = 4p,c = 7p\)

Hence, \(\frac{{a + b + c}}{a} = \frac{{3p + 4p + 7p}}{{3p}} = \frac{{14p}}{{3p}}\)

\(\Rightarrow \frac{{a + b + c}}{a} = \frac{{14}}{3} = 4\frac{2}{3}\)