Question

If 343 is the third proportional of a and b, where a : b = 1 : 7, then the value of a + b is

(a) 14
(b) 24
(c) 56
(d) 63

Answer 1

It is given that,
$\frac{a}{b}=\frac{1}{7}...\left(1\right)$

According to the question,
$$\begin{gathered} a:b::b:343 \\ \Rightarrow \frac{a}{b}=\frac{b}{343} \\ \Rightarrow \frac{1}{7}=\frac{b}{343}\left[\mathrm{From}\left(1\right)\right] \\ \Rightarrow \frac{1\times 343}{7}=\frac{b\times 343}{343} \\ \Rightarrow 49=b \end{gathered}$$

Now,
$$\begin{gathered} \frac{a}{b}=\frac{1}{7} \\ \Rightarrow \frac{a}{49}=\frac{1}{7} \\ \Rightarrow \frac{a\times 49}{49}=\frac{1\times 49}{7} \\ \Rightarrow a=7 \end{gathered}$$

Thus, a + b = 7 + 49 = 56

Hence, the correct option is (c).