Find the ratio compounded of
(1) the ratio 2a, 3b, and the duplicate of $9 b^{2} : a b .$
(2) the subduplicate ratio of 64 : 9, and the ratio 27 : 56.
(3) the duplicate ratio of $\frac{2 a}{b} : \frac{\sqrt{C} a^{2}}{b^{2}},$ and the ratio 3ax : 2by .

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Solution

$(1)$ Duplicate of $9 b^{2} : a b$ is equal to $81 b^{4} : a^{2} b^{2}$
The compound of $2 a : 3 b$ and the duplicate of $9 b^{2} : a b$ is $2 a \times 81 b^{4} : 3 b \times a^{2} b^{2} = 54 b : a$
$(2)$ Sub duplicate ratio of $64 : 9$ is $8 : 3$
The compound of the sub duplicate ratio of $64 : 9$ and the ratio $27 : 56$ is $8 \times 27 : 3 \times 56 = 9 : 7$
$(3)$ Duplicate ratio of $\frac{2 a}{b} : \frac{\sqrt{c} a^{2}}{b^{2}}$ is equal to $\frac{4 a^{2}}{b^{2}} : \frac{c a^{4}}{b^{4}}$
The compound of the duplicate of ratio $\frac{2 a}{b} : \frac{\sqrt{c} a^{2}}{b^{2}}$ and the ratio $3 a x : 2 b y$ is $\frac{4 a^{2}}{b^{2}} \times 3 a x : \frac{c a^{4}}{b^{4}} \times 2 b y = 6 b x : a c y$

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The ratio compounded of the duplicate ratio of 8 : 7, the sub-duplicate of 9:64 and the reciprocal of 24 : 49 is

Find the compounded ratio of the duplicate ratio of 3 : 5, the reciprocal ratio of 4 : 25, and the sub-duplicate ratio of 16 : 81.

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