Question

The ratio compounds of $4:9$, the duplicate ratio of $3:4$, the triplicate ratio of $2:3$ and $9:7$ is

• A. $2:7$
• B. $7:2$
• C. $2:21$
• D. $oneofthese$

Answer 1

The correct option is C $2:21$

Duplicate of ratio $3:4=\frac{3^2}{4^2}=9:16$

Triplicate ratio of $2:3=\frac{2^3}{3^3}=8:27$

Now we have $4$ ratios, i.e.,

$\frac{4}{9},\frac{9}{16},\frac{8}{27}$ and $\frac{9}{7}$

Compounded ratio of these ratios $=\frac{4\times 9\times 8\times 9}{9\times 16\times 27\times 7}=\frac{2}{21}$