ABC26GN3007 · Ratio and Proportion
Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
If $x: y=3: 2$, then the ratio $\left(2 x^{2}+3 y^{2}\right):\left(3 x^{2}-2 y^{2}\right)$ is equal to
(a)5 : 3
(b)6 : 5
(c)12 : 5
(d)30 : 19
Answer
Explanation
$$\begin{aligned} & \frac{x}{y}=\frac{3}{2} \Rightarrow \frac{x^{2}}{y^{2}}=\frac{9}{4} \Rightarrow \frac{2 x^{2}+3 y^{2}}{3 x^{2}-2 y^{2}} \\ & \quad=\frac{2\left(\frac{x^{2}}{y^{2}}\right)+3}{3\left(\frac{x^{2}}{y^{2}}\right)-2}=\frac{2 \times \frac{9}{4}+3}{3 \times \frac{9}{4}-2}=\frac{15}{2} \times \frac{4}{19}=\frac{30}{19} \\ & \Rightarrow\left(2 x^{2}+3 y^{2}\right):\left(3 x^{2}-2 y^{2}\right)=30: 19 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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