Ratio and Proportion — MATHS STD 7 — Question

2. 20 : 15 : 12

Solution:

As, $\frac{1}{\text{a}}:\frac{1}{\text{b}}:\frac{1}{\text{c}}=3:4:5$

$\Rightarrow\frac{1}{\text{a}}:\frac{1}{\text{b}}=3:4$ and $\frac{1}{\text{b}}:\frac{1}{\text{c}}=4:5$

$\Rightarrow\frac{1}{\text{a}}\div\frac{1}{\text{b}}=\frac{3}{4}$ and $\frac{1}{\text{b}}\div\frac{1}{\text{c}}=\frac45$

$\Rightarrow\frac{1}{\text{a}}\times\frac{\text{b}}{1}=\frac{3}{4}$ and $\frac{1}{\text{b}}\times\frac{\text{c}}{1}=\frac{4}{5}$

$\Rightarrow\frac{\text{b}}{\text{a}}=\frac{3}{4}$ and $\frac{\text{c}}{\text{b}}=\frac{4}{5}$

$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{4}{3}$ and $\frac{\text{b}}{\text{c}}=\frac{5}{4}$ (Reciprocal of both sides)

$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{4\times5}{3\times5}$ and $\frac{\text{b}}{\text{c}}=\frac{5\times3}{4\times3}$

$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{20}{15}$ and $\frac{\text{b}}{c}=\frac{15}{12}$

$\Rightarrow\text{a}:\text{b}=20:15$ and $\text{b}:\text{c}=15:12$

$\therefore\text{a}:\text{b}:\text{c}=20:15:12$

Hence, the correct alternative is option (b).