Question

Fill in the blanks.

(i) If A : B = 2 : 3 and B : C = 4 : 5, then C : A = ...... .
(ii) If 16% of A = 20% of B, then A : B = ...... .
(iii) If $A=\frac{1}{3}BandB=\frac{1}{2}C,$ then A : B : C = ...... .
(iv) If A : B = 5 : 7 and B : C = 6 : 11, then A : B : C = ...... .

Answer 1

(i) 15 : 8

$\frac{A}{C}=\frac{A}{B}\times \frac{B}{C}=\frac{2}{3}\times \frac{4}{5}=\frac{8}{15}$

∴ C : A=15 : 8

(ii) 5 : 4

$$\begin{gathered} \frac{16}{100}A=\frac{20}{100}B \\ \Rightarrow \frac{A}{B}=\frac{20}{16}=\frac{5}{4} \end{gathered}$$

(iii) 1 : 3 : 6

$A:B:C=\frac{1}{3}B:B:2B=1:3:6$

(iv) 30 : 42 : 77

$$\begin{gathered} \frac{A}{B}=\frac{5\times 6}{7\times 6}=\frac{30}{42} \\ \Rightarrow \frac{B}{C}=\frac{6\times 7}{11\times 7}=\frac{42}{77}\Rightarrow A:B:C=30:42:77 \end{gathered}$$