If X and Y are in the ratio of $2 : 3$ , $(2 X + 3 Y^{2}) : (3 X^{2} + 2 Y)$ would be in the ratio of_____.

31 : 18

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21 : 13

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18 : 31

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13 : 10

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Solution

The correct option is A $31 : 18$
solution:
$\frac{x}{y} = \frac{2}{3}$
if x= 2t and y = 3t then solving
$\frac{2 x + 3 y^{2}}{3 x^{2} + 2 y} = \frac{4 t + 27 t^{2}}{3 x^{2} + 3 x} = \frac{4 + 27 t}{12 t + 6}$
if we consider t =1 we get
$\frac{2 x + 3 y^{2}}{3 x^{2} + 2 y} = \frac{31}{18}$
hence the correct option: A

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Similar questions

\frac{x + 1}{2} = \frac{y}{3} = \frac{z - 1}{6}

10 x + 2 y - 11 z = 3

$x$	$19$	$21$	$23$	$25$	$27$	$29$	$31$
$f$	$13$	$15$	$16$	$18$	$16$	$15$	$13$

x

y

$x$	$1$	$2$	$3$	$4$	$5$
$y$	$3$	$7$	$13$	$21$	$31$

Age( in years)	$19$	$21$	$23$	$25$	$27$	$29$	$31$
Number of persons	$13$	$15$	$20$	$18$	$16$	$17$	$13$

Find the number of terms in the following AP: $18, \frac{31}{2}, 13, . . . - 47$

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