Question

FIND THE RATIO COMPOUNDED OF 25:18,THE SUBDUPLICATE RATIO OF 81:49, THE TRIPLICATE RATIO OF 2:3 AND THE DUPLICATE RATIO OF 7:5.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{duplicate}\mathrm{ratio}\mathrm{of}\mathrm{a}:\mathrm{b}\mathrm{is}{\mathrm{a}}^2:{\mathrm{b}}^2. \\ \mathrm{so}\mathrm{duplicate}\mathrm{ratio}\mathrm{of}7:5\mathrm{is}{7}^2:5^2=49:25 \\ \mathrm{We}\mathrm{know}\mathrm{triplicate}\mathrm{ratio}\mathrm{of}\mathrm{a}:\mathrm{b}\mathrm{is}{\mathrm{a}}^3:{\mathrm{b}}^3 \\ \mathrm{so}\mathrm{triplicate}\mathrm{ratio}\mathrm{of}2:3\mathrm{is}{2}^3:3^3=8:27 \\ \mathrm{we}\mathrm{know}\mathrm{sub}-\mathrm{duplicate}\mathrm{ratio}\mathrm{of}\mathrm{a}:\mathrm{b}\mathrm{is}\sqrt{\mathrm{a}}:\sqrt{\mathrm{b}} \\ \mathrm{so}\mathrm{subduplicate}\mathrm{ratio}\mathrm{of}81:49=\sqrt{81}:\hspace{0.17em}\sqrt{49}=9:\hspace{0.17em}7 \\ \mathrm{So},\mathrm{required}\mathrm{compounded}\mathrm{ratio}=25\times 9\times 8\times 49:18\times 7\times 27\times 25=\frac{25\times 9\times 8\times 49}{18\times 7\times 27\times 25}=\frac{28}{27}=28:27 \end{gathered}$$