Question

Mark the correct alternative in the following question:

If a : b = 5 : 7 and b : c = 6 : 11, then a : b : c =

(a) 35 : 49 : 66 (b) 30 : 42 : 77 (c) 30 : 42 :55 (d) None of these

Answer 1

$$\begin{gathered} \mathrm{As},a:b=5:7\mathrm{and}b:c=6:11 \\ \Rightarrow \frac{a}{b}=\frac{5}{7}\mathrm{and}\frac{b}{c}=\frac{6}{11} \\ \Rightarrow \frac{a}{b}=\frac{5\times 6}{7\times 6}\mathrm{and}\frac{b}{c}=\frac{6\times 7}{11\times 7} \\ \Rightarrow \frac{a}{b}=\frac{30}{42}\mathrm{and}\frac{b}{c}=\frac{42}{77} \\ \Rightarrow a:b=30:42\mathrm{and}b:c=42:77 \\ \therefore a:b:c=30:42:77 \end{gathered}$$

Hence, the correct alternative is option (b).