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Question Number 38636 by pieroo last updated on 27/Jun/18

$$\mathrm{Three}\mathrm{variables}\mathrm{u},\mathrm{v}\mathrm{and}\mathrm{w}\mathrm{are}\mathrm{related}\mathrm{such}\mathrm{that}$$$$\mathrm{u}\mathrm{varies}\mathrm{directly}\mathrm{as}\mathrm{v}\mathrm{and}\mathrm{inversely}\mathrm{as}\mathrm{the}\mathrm{square}\mathrm{of}$$$$\mathrm{w}.\mathrm{If}\mathrm{v}\mathrm{increases}\mathrm{by}15\mathrm{\%}\mathrm{and}\mathrm{w}\mathrm{decreased}\mathrm{by}10\mathrm{\%},$$$$\mathrm{find}\mathrm{the}\mathrm{percentage}\mathrm{change}\mathrm{in}\mathrm{u}.$$

Answered by MrW3 last updated on 28/Jun/18

$$u=k\frac{v}{w^2}$$$$v_2=1.15v_1\left(increaseby15\mathrm{\%}\right)$$$$w_2=0.90w_1\left(decreaseby10\mathrm{\%}\right)$$$$u_2=k\frac{1.15v_1}{0.{90}^2{w}_1^2}=\frac{1.15}{0.{90}^2}\times k\frac{v_1}{w_1^2}=\frac{1.15}{0.{90}^2}{u}_1=1.42u_1$$$$\Rightarrow uincreasesby42\mathrm{\%}.$$

Commented by pieroo last updated on 28/Jun/18

$$\mathrm{Thanks}\mathrm{Sir}.$$

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