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Ratio and Proportion

Question

If $(\begin{matrix} 4 x^{2} - 3 y^{2} \end{matrix}) : (\begin{matrix} 2 x^{2} + 5 y^{2} \end{matrix}) = 12 : 19$ , then $x : y$ is
$2 : 3$
$1 : 2$
$3 : 2$
$1 : 4$

A

1 : 4

B

2 : 3

C

1 : 2

D

3 : 2

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Solution

Verified by Toppr

$\frac{4 x^{2} - 3 y^{2}}{2 x^{2} + 5 y^{2}} = \frac{12}{19}$
$19 (4 x^{2} - 3 y^{2}) = 12 (2 x^{2} + 5 y^{2})$
$⟹ 52 x^{2} = 117 y^{2}$
$⟹ 4 x^{2} = 9 y^{2}$
$⟹ \frac{x^{2}}{y^{2}} = \frac{9}{4}$
$⟹ \frac{x}{y} = \frac{3}{2}$

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Similar Questions

Q1

If

(\begin{matrix} 4 x^{2} - 3 y^{2} \end{matrix}) : (\begin{matrix} 2 x^{2} + 5 y^{2} \end{matrix}) = 12 : 19

, then

x : y

is

View Solution

Q2

If (4x²–3y²):(2x²+5y²)=12:19,find x:y

View Solution

Q3

If

({3 x}^{2} - {3 y}^{2}) : ({2 x}^{2} + {5 y}^{2}) = 12 : 19

, then

(x : y)

is:

View Solution

Q4

If

x

and

y

both are positive and

(2 x^{2} - 5 y^{2}) : x y = 1 : 3

, find

x : y

.

View Solution

Q5

If

l_{1}

is the tangent to

2 x^{2} + 3 y^{2} = 35

at

(4, - 1)

and

l_{2}

is the tangent to

4 x^{2} + y^{2} = 25

at

(2, - 3),

then distance between

l_{1}

and

l_{2}

is :

View Solution