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Find the sub – triplicate ratio of the following:(i) 512:216(ii) {{m}^{3}}{{n}^{6}}:{{m}^{6}}{{n}^{3}}
Class 10 | Frank | Guides | ICSE | Maths | Ratio and Proportion
Find the sub – triplicate ratio of the following:(i) 512:216(ii) {{m}^{3}}{{n}^{6}}:{{m}^{6}}{{n}^{3}}

The ratio is used for comparing two quantities of the sane kind.

The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in proportion.

The concept of ratio and proportion is majorly based on ratios and fractions.  

Solution:

Given, 512:216

 {{=}^{3}}\sqrt{512}{{:}^{3}}\sqrt{216}

={{\left( {{8}^{3}} \right)}^{1/3}}:{{\left( {{6}^{3}} \right)}^{1/3}}

=8:6

=8/6

=4/3

={{\left( {{8}^{3}} \right)}^{1/3}}.{{\left( {{6}^{3}} \right)}^{1/3}}

=8:6

=8/6

=4/3

Therefore, sub – triplicate ratio is 4:3.

Solution:

Given, {{m}^{3}}{{n}^{6}}:{{m}^{6}}{{n}^{3}}

{{=}^{3}}\sqrt{\left( {{m}^{3}}{{n}^{6}} \right)}{{:}^{3}}\sqrt{\left( {{m}^{6}}n3 \right)}

={{\left( {{m}^{3}}{{n}^{6}} \right)}^{1/13}}:{{\left( {{m}^{6}}{{n}^{3}} \right)}^{1/13}}

=m{{n}^{2}}:{{m}^{2}}n

=m{{n}^{2}}/{{m}^{2}}n

=n/m

Therefore, sub – triplicate ratio isn:m

i

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