MCQ
If $a : b = 5 : 7$ and $b : c = 6 : 11,$ then $a : b : c =$
- A$5 : 4 : 3$
- ✓$20 : 15 : 12$
- C$9 : 12 : 15$
- D$12 : 15 : 20$
As, $\text{a}:\text{b}=5:7$ and $\text{b}:\text{c}=6:11$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac57$ and $\frac{\text{b}}{\text{c}}=\frac{6}{11}$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{5\times6}{7\times6}$ and $\frac{\text{b}}{\text{c}}=\frac{6\times7}{11\times7}$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{30}{42}$ and $\frac{\text{b}}{\text{c}}=\frac{42}{77}$
$\Rightarrow\text{a}:\text{b}=30:42$ and $\text{b}:\text{c}=42:77$
$\therefore\text{a}:\text{b}:\text{c}=30:42:77$
Hence, the correct alternative is option $(b).$
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