If A : B = $\dfrac{1}{4} : \dfrac{1}{5}$ and B : C = $\dfrac{1}{7} : \dfrac{1}{6}$, find A : B : C.

Given, A : B = $\dfrac{1}{4} : \dfrac{1}{5}$ = 5 : 4 and B : C = $\dfrac{1}{7} : \dfrac{1}{6}$ = 6 : 7

To find A : B : C, we will make B same in both cases.

Taking L.C.M. of two values of B i.e. 4 and 6 = 12

$\text{So }, \dfrac{A}{B} = \dfrac{5 \times 3}{4 \times 3} = \dfrac{15}{12} = 15 : 12 \\[0.5em] \text{and } \dfrac{B}{C} = \dfrac{6}{7} = \dfrac{6 \times 2}{7 \times 2} = \dfrac{12}{14} = 12 : 14 \\[0.5em]$

∴ A : B : C = 15 : 12 : 14

Hence, the ratio of A : B : C is 15 : 12 : 14.