ABC26GN2944 · Ratio and Proportion
Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
$x^{2}$ varies directly as $y^{3}$ and when $x=6, y=3$. Deduce the relation between $x$ and $y$.
Answer
Explanation
$x^2 \propto y^3 \Rightarrow x^2=ky^3$ for some constant $k$. When $x=6$ and $y=3$, we have: $$x^2=ky^3 \Rightarrow 6^2=k\times 3^3 \Rightarrow 36=27k \Rightarrow k=\frac{36}{27}=\frac{4}{3}.$$ $$\therefore \quad x^2=\frac{4}{3}y^3 \Rightarrow 3x^2=4y^3.$$
Explanation as extracted from the printed page; notation may be imperfect.
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