Maharashtra State BoardSSC (English Medium) 8th Standard
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X ∝ 1 √ Y and When X = 40 Then Y = 16. If X = 10, Find Y. - Mathematics

Sum

x ∝ \[\frac{1}{\sqrt{y}}\]  and when x = 40 then y = 16. If x = 10, find y.

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Solution

It given that \[x \propto \frac{1}{\sqrt{y}}\] . 

∴ \[x = \frac{k}{\sqrt{y}}\] , where k is constant of variation

⇒ \[x \times \sqrt{y} = k\]

When x = 40, y = 16.
∴ \[k = 40 \times \sqrt{16} = 40 \times 4 = 160\]

So, the equation of variation is \[x\sqrt{y} = 160\]

When x = 10, 

\[10\sqrt{y} = 160\] 

\[ \Rightarrow \sqrt{y} = 16\] 

\[ \Rightarrow y =  {16}^2  = 256\]

Concept: Inverse Variation
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APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 7 Variation
Practice Set 7.2 | Q 5 | Page 39
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