Question

Find the

$\left(vi\right)$ Ratio compounded of the duplicate ratio of 5:6, the reciprocal ratio of 25:42 and the sub-duplicate ratio of 36:49

Answer 1

Step: Find the compounded ratio

We know, compounded ratio =

$\frac{\text{Product of first number in all ratios}}{\text{Product of 2nd number in all ratios}}$

Duplicate ratio of $5:6=5^2:6^2$

$=25:36$

Reciprocal ratio of $25:42=\frac{1}{25}:\frac{1}{42}$

$=42:25$

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

$=6:7$

$\therefore$ Compounded ratio $=\frac{25\times 42\times 6}{36\times 25\times 7}$

$=\frac{25\times 6\times 6}{36\times 25}$

$=\frac{25\times 36}{36\times 25}$

$=\frac{1}{1}$

Hence, the compounded ratio is $1:1$