MCQ
If $\frac{\text{a}}{2}=\frac{\text{b}}{3}=\frac{\text{c}}{4},$ then $\text{a}:\text{b}:\text{c}=$
- ✓$2 : 3 : 4$
- B$4 : 3 : 2$
- C$3 : 2 : 4$
- DNone of these.
✓
Answer
Correct option: A.
$2 : 3 : 4$
As, $\frac{\text{a}}{2}=\frac{\text{b}}{3}=\frac{\text{c}}{4}$
$\Rightarrow\frac{\text{a}}{2}=\frac{\text{b}}{3}$ and $\frac{\text{b}}{3}=\frac{\text{c}}{4}$
$\Rightarrow3\text{a}=2\text{b}$ and $4\text{b}=3\text{c} ($By cross multiplication$)$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{2}{3}$ and $\frac{\text{b}}{\text{c}}=\frac{3}{4}$
$\Rightarrow\text{a}:\text{b}=2:3$
$\therefore\text{a}:\text{b}:\text{c}=2:3:4$
Hence, the correct alternative is option $(a).$
$\Rightarrow\frac{\text{a}}{2}=\frac{\text{b}}{3}$ and $\frac{\text{b}}{3}=\frac{\text{c}}{4}$
$\Rightarrow3\text{a}=2\text{b}$ and $4\text{b}=3\text{c} ($By cross multiplication$)$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{2}{3}$ and $\frac{\text{b}}{\text{c}}=\frac{3}{4}$
$\Rightarrow\text{a}:\text{b}=2:3$
$\therefore\text{a}:\text{b}:\text{c}=2:3:4$
Hence, the correct alternative is option $(a).$
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