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X ∝ 1 √ Y and When X = 40 Then Y = 16. If X = 10, Find Y. - SSC (English Medium) Class 8 - Mathematics

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Question

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

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, 

\[10\sqrt{y} = 160\] 

\[ \Rightarrow \sqrt{y} = 16\] 

\[ \Rightarrow y =  {16}^2  = 256\]

  Is there an error in this question or solution?

APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 7: Variation
Practice Set 7.2 | Q: 5 | Page no. 39
Solution X ∝ 1 √ Y and When X = 40 Then Y = 16. If X = 10, Find Y. Concept: Inverse Variation.
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