1. Find two numbers such that their mean proportion is 8 and third proportion is 64.
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By: anil on 05 May 2019 02.10 am
Three numbers a,b,c are in proportion iff $$b^2 = ac$$ where $$b$$ is the mean proportion and $$c$$ is the third proportion Mean proportion of two numbers $$x$$ and $$y$$ = 8 => $$xy = (8)^2 = 64$$ ---------------(i) Third proportion = 64 => $$y^2 = x imes 64$$ -------------(ii) Substituting value of $$x$$ from equation(i) in equation(ii), we get : => $$y^2 = frac{64}{y} imes 64$$ => $$y^3 = (2)^6 imes (2)^6 = (2)^{6 + 6}$$ => $$y = (2)^{frac{12}{3}} = 2^4 = 16$$ Substituting it in equation(i), => $$x = frac{64}{16} = 4$$ => Ans - (D)
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