Question 11 MarkFind the reciprocal ratio of 3: 5AnswerThe reciprocal ratio of 3: 5 =5 : 3View full question & answer→
Question 21 MarkFind the sub-triplicate ratio of 216: 343AnswerSub-triplicate ratio 216: 343 $=\sqrt[3]{216}: \sqrt[3]{343}=6: 7$View full question & answer→
Question 31 MarkFind the sub-duplicate ratio of $9x^2a^4: 25y^6b^2$AnswerThe sub-duplicate ratio of $9 x^2 a^4: 25 y^6 b^2=$$\sqrt{9 x^2 a^4}: \sqrt{25 y^6 b^2}=3 x a^2: 5 y^3 b$View full question & answer→
Question 41 MarkFind the triplicate ratio of 2a: 3bAnswerTriplicate ratio of $2 a: 3 b=(2 a)^3:(3 b)^3=8 a^3: 27 b^3$View full question & answer→
Question 51 MarkFind the duplicate ratio of $2 \sqrt{2}: 3 \sqrt{5}$AnswerDuplicate ratio of $2 \sqrt{2}: 3 \sqrt{5}=(2 \sqrt{2})^2:(3 \sqrt{5})^2=8: 45$View full question & answer→
Question 61 MarkIf a : b = c : d, prove that: 5a + 7b : 5a – 7b = 5c + 7d : 5c – 7d.AnswerGiven $\frac{a}{b}=\frac{c}{d}$$\Rightarrow \frac{5 a}{7 b}=\frac{5 c}{7 d}$ (Multiplying each side by 5/7)$\Rightarrow \frac{5 a+7 b}{5 a-7 b}=\frac{5 c+7 d}{5 c-7 d}$ (By componendo and dividendo)View full question & answer→
Question 71 MarkUsing properties of proportion solve for x: $\frac{3 x+\sqrt{9 x^2-5}}{3 x-\sqrt{9 x^2-5}}=5$Answer$\frac{3 x+\sqrt{9 x^2-5}}{3 x-\sqrt{9 x^2-5}}=5$ Applying componendo and dividendo $\frac{3 x+\sqrt{9 x^2-5}+3 x-\sqrt{9 x^2-5}}{3 x \sqrt{9 x^2-5}-3 x+\sqrt{9 x^2-5}}=\frac{5+1}{5-1} $ $ \frac{6 x}{2 \sqrt{9 x^2-5}}=\frac{6}{4} $ $ \frac{3 x}{\sqrt{9 x^2-5}}=\frac{3}{2}$ $ \frac{x}{\sqrt{9 x^2-5}}=\frac{1}{2}$ Squaring both sides $\frac{x^2}{9 x^2-5}=\frac{1}{4}$ $4 x^2-9 x^2=-5$ $-5 x^2=-5 $ $5 x^2=5 $ $ x^2=1 $ $x=\sqrt{1} $ $ x=1$View full question & answer→
Question 81 MarkFind the reciprocal ratio of $\frac{x}{3}: \frac{y}{7}$Answerreciprocal ratio of $\frac{x}{3}: \frac{y}{7}=\frac{1}{\frac{x}{3}}: \frac{1}{\frac{y}{7}}=\frac{3}{x}: \frac{7}{y}=\frac{\frac{3}{x}}{\frac{7}{y}}=\frac{3 y}{7 x}=3 y: 7 x$View full question & answer→
Question 91 MarkFind the reciprocal ratio of:5 : 8AnswerReciprocal ratio of $5: 8=\frac{1}{5}: \frac{1}{8}=8: 5$View full question & answer→
Question 101 MarkFind the sub-triplicate ratio of $x^3: 125 y^3$AnswerSub-triplicate ratio of $x^3: 125 y^3=125 y^3=\sqrt[3]{x^3}: \sqrt[3]{125 y^3}=x: 5 y$View full question & answer→
Question 111 MarkFind the sub-triplicate ratio of 64: 27AnswerFind the sub-triplicate ratio of $64: 27=\sqrt[3]{64}: \sqrt[3]{27}=4: 3$View full question & answer→
Question 121 MarkFind the sub-duplicate ratio of $(x-y)^4:(x+y)^6$AnswerSub-duplicate ratio of $(x-y)^4:(x+y)^6$$=\sqrt{(x-y)^4}: \sqrt{(x+y)^6}=(x-y)^2:(x+y)^3$View full question & answer→
Question 131 MarkFind the sub-duplicate ratio of 9: 16AnswerSub-duplicate ratio of $9: 16=\sqrt{9}: \sqrt{16}=3: 4$View full question & answer→
Question 141 MarkFind the triplicate ration of $\frac{m}{2}: \frac{n}{3}$AnswerTriplicate ratio of $\frac{m}{2}: \frac{n}{3}$$=\left(\frac{m}{2}\right)^3:\left(\frac{n}{3}\right)^3$$=\frac{m^3}{8}: \frac{n^3}{27}$$=\frac{\frac{m^3}{8}}{\frac{n^3}{27}}=27 m^3: 8 n^3$View full question & answer→
Question 151 MarkFind the triplicate ratio of 1 : 3AnswerTriplicate ratio of $1: 3=1^3: 3^3=1: 27$View full question & answer→
Question 161 MarkFind the duplicate ratio of $3 \sqrt{3}: 2 \sqrt{5}$AnswerDuplicate ratio of $3 \sqrt{3}: 2 \sqrt{5}=(3 \sqrt{3})^2:(2 \sqrt{5})^2=27: 20$View full question & answer→
Question 171 MarkFind the duplicate ratio of 3: 4AnswerDuplicate ratio of 3 : 4 = 32 : 42 = 9 : 16View full question & answer→
Question 181 MarkFind the compound ration of $2a: 3b$, $mn: x^2$ and $x: n$AnswerRequired compound ratio $=2 a \times mn \times x : 3 b \times x^2 \times n ^`$ $=\frac{2 a \times m n \times x}{3 b \times x^2 \times n}$ $=\frac{2 a m}{3 b x}=2 a m: 3 b x$View full question & answer→
Question 191 MarkFind the compound ratio of $2 : 3, 9: 14$ and $14: 27$AnswerRequired compound ration = 2 x 9 x 14 : 3 x 14 x 27 $=\frac{2 \times 9 \times 14}{3 \times 14 \times 27} $ $ =\frac{2}{9}=2: 9$View full question & answer→