What numbers must be subtracted from 6, 7, 18, 22, so that they will be in proportion ?

Dear Student,

Please find below the solution to the asked query:

We know : Numbers are in continued proportion

If  a : b =  c : d

Suppose x is subtracted from each of the number

 Then

( a - x ) : ( b - x ) = ( c - x ) : ( d - x )

Now we substitute values and get

$\Rightarrow$( 6 - x  ) : ( 7 - x ) = ( 18 - x ) : ( 22 - x )

$$\begin{gathered} \Rightarrow \frac{\left( 6 - x \right)}{\left( 7 - x \right)} = \frac{\left( 18 - x \right)}{\left( 22 - x \right)} \\ \Rightarrow \left( 6 - x \right)\left( 22 - x \right) = \left( 18 - x \right)\left( 7 - x \right) \\ \Rightarrow 132 - 6 x - 22 x + x^2 = 126 - 18 x - 7 x + x^2 \\ \Rightarrow 132 - 28x + x^2 = 126 - 25 x + x^2 \\ \Rightarrow 3 x=6 \\ \Rightarrow x=\frac{6}{3} \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{2}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

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