Login/Sign Up
Home » Find the mean proportion of: (iii)     (iv)    
Find the mean proportion of: (iii)

    \[\mathbf{8}.\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{2}.\mathbf{5}\]

(iv)

    \[\left( a\text{ }\text{ }b \right)\text{ }and\text{ }({{a}^{3}}~\text{ }{{a}^{2}}b),\text{ }a>b\]

Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
Find the mean proportion of: (iii)

    \[\mathbf{8}.\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{2}.\mathbf{5}\]

(iv)

    \[\left( a\text{ }\text{ }b \right)\text{ }and\text{ }({{a}^{3}}~\text{ }{{a}^{2}}b),\text{ }a>b\]

(iii) Consider x as the mean proportion of

    \[8.1\text{ }and\text{ }2.5\]

    \[8.1:\text{ }x\text{ }::\text{ }x:\text{ }2.5\]

It can be written as

    \[\begin{array}{*{35}{l}} {{x}^{2}}~=\text{ }8.1\text{ }\times \text{ }2.5\text{ }=\text{ }20.25 \\ x\text{ }=\text{ }\surd 20.25\text{ }=\text{ }4.5 \\ \end{array}\]

Therefore, mean proportion of

    \[8.1\text{ }and\text{ }2.5\text{ }is\text{ }4.5\]

(iv) Consider x as the mean proportion of

    \[\left( a\text{ }\text{ }b \right)\text{ }and\text{ }({{a}^{3}}~\text{ }{{a}^{2}}b),\text{ }a>b\]

    \[\left( a\text{ }\text{ }b \right):\text{ }x\text{ }::\text{ }({{a}^{3}}~\text{ }{{a}^{2}}b)\]

It can be written as

    \[{{x}^{2}}~=\text{ }\left( a\text{ }\text{ }b \right)\text{ }({{a}^{3}}~\text{ }{{a}^{2}}b)\]

So we get

    \[\begin{array}{*{35}{l}} {{x}^{2}}~=\text{ }\left( a\text{ }\text{ }b \right)\text{ }{{a}^{2}}~\left( a\text{ }\text{ }b \right) \\ {{x}^{2}}~=\text{ }{{a}^{2}}~{{\left( a\text{ }\text{ }b \right)}^{2}} \\ \end{array}\]

Here

x = a (a – b)

Therefore, mean proportion of (a – b) and

    \[({{a}^{3}}~\text{ }{{a}^{2}}b),\text{ }a>b\text{ }is\text{ }a\text{ }(ab)\]

i

More Material