Question

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

Answer 1

We know that, if a : b is a ratio, then its sub-duplicate ratio is √a : √b.
If a : b is a ratio, then its triplicate ratio is $a^3:b^3$.
And reciprocal ratio is the ratio of the reciprocals of two quantities.

So, sub-duplicate ratio of 36 : 49 $=\sqrt{36}:\sqrt{49}=6:7$

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

And triplicate ratio of 5 : 4 $=(5{)}^3:(4{)}^3$ $=125:64$

Therefore, the required compounded ratio

$=(6\times 28\times 125):(7\times 15\times 64)$

$=\frac{6\times 28\times 125}{7\times 15\times 64}$

$=\frac{25}{8}=25:8$