Question

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

Answer 1

Find the reciprocal ratio of $15:28$

Reciprocal ratio of $15:28\text{is}\frac{1}{15}:\frac{1}{28}$

$=28:15$

Find the sub-duplicate ratio of $36:49$

Sub-duplicate ratio is the square root of given ratio.

Sub-duplicate ratio $=\sqrt{36}:\sqrt{49}$
$=6:7$

Find the triplicate ratio of $5:4$

Triplicate ratio is the cube of the given ratio.

Triplicate ratio of $5:4\text{is}{5}^3:4^3$

$=125:64$

Find the compound ratio of the obtained ratios

Compound ratio is ratio of the product of first number of all ratios to the product of a second number.

Now, compound ratio $=\frac{(28\times 6\times 125)}{15\times 7\times 64}$

$=\frac{4\times 3\times 2\times 125}{3\times 5\times 4\times 16}$

$=\frac{25}{8}$

Hence, the compound ratio is $25:8$.