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Find the sub-triplicate ratio of (i)

    \[\mathbf{1}:\text{ }\mathbf{216}\]

(ii)

    \[\mathbf{1}/\mathbf{8}:\text{ }\mathbf{1}/\mathbf{125}\]

Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
Find the sub-triplicate ratio of (i)

    \[\mathbf{1}:\text{ }\mathbf{216}\]

(ii)

    \[\mathbf{1}/\mathbf{8}:\text{ }\mathbf{1}/\mathbf{125}\]

(i)

    \[\mathbf{1}:\text{ }\mathbf{216}\]

We know that

Sub-triplicate ratio of

    \[1:\text{ }216\text{ }=\sqrt[3]{1}:\sqrt[3]{216}\]

By further calculation

    \[\begin{array}{*{35}{l}} =\text{ }{{({{1}^{3}})}^{1/3}}:\text{ }{{({{6}^{3}})}^{1/3}} \\ =\text{ }1:\text{ }6 \\ \end{array}\]

(ii)

    \[1/8:\text{ }1/125\]

We know that

Sub-triplicate ratio of

    \[1/8:\text{ }1/125\text{ }=\text{ }{{\left( 1/8 \right)}^{1/3}}:\text{ }{{\left( 1/125 \right)}^{1/3}}\]

It can be written as

    \[=\text{ }{{[{{\left( 1/2 \right)}^{3}}]}^{1/3}}:\text{ }{{[{{\left( 1/5 \right)}^{3}}]}^{1/3}}\]

So we get

    \[\begin{array}{*{35}{l}} =\text{ }{\scriptscriptstyle 1\!/\!{ }_2}:\text{ }1/5 \\ =\text{ }5:\text{ }2 \\ \end{array}\]

i

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