Find the ratio compounded of the reciprocal ratio of 15 : 28, the sub-duplicate ratio of 36 : 49 and the triplicate ratio of 5 : 4.

Reciprocal ratio of 15 : 28,

$\Rightarrow \dfrac{1}{15} : \dfrac{1}{28} \\[1em] \Rightarrow \dfrac{\dfrac{1}{15}}{\dfrac{1}{28}} \\[1em] \Rightarrow \dfrac{28}{15} \\[1em] \Rightarrow 28 : 15.$

Sub-duplicate ratio of 36 : 49,

$\Rightarrow \sqrt{36} : \sqrt{49} \\[1em] \Rightarrow 6 : 7.$

Triplicate ratio of 5 : 4,

= 5³ : 4³

= 125 : 64.

Compound ratio,

$= \dfrac{28}{15} \times \dfrac{6}{7} \times \dfrac{125}{64} \\[1em] = \dfrac{25}{8} \\[1em] = 25 : 8.$

Hence, compounded ratio = 25 : 8.