Question

Find the ratio of (4x - 5y) & (5y + 2y) if (2x - y) : (2x + 4y) = 1:4

Please explain this to me fully!

And please don't spam!

I need correct answer urgently with explanation!...

________________

And thank ya'again for your answer!! :) ​

Answer 1

EXPLANATION.

Ratio of (4x - 5y) & (5x + 2y).

If (2x - y) : (2x + 4y) = 1 : 4.

As we know that,

⇒ (2x - y) : (2x + 4y) = 1 : 4.

⇒ (2x - y)/(2x + 4y) = 1/4.

⇒ 4(2x - y) = 1(2x + 4y).

⇒ 8x - 4y = 2x + 4y.

⇒ 8x - 2x = 4y + 4y.

⇒ 6x = 8y.

⇒ 3x = 4y.

⇒ x = 4y/3.

To find :

⇒ (4x - 5y).

⇒ (4 x 4y/3 - 5y).

⇒ (16y/3 - 5y).

⇒ (16y - 15y/3). = y/3. - - - - - (1).

⇒ (5x + 2y).

⇒ (5 x 4y/3 + 2y).

⇒ (20y/3 + 2y).

⇒ (20y + 6y)/3.

⇒ (26y/3). - - - - - (2).

Ration of equation (1) : (2).

⇒ y/3 : 26y/3.

⇒ 1 : 26 = 1/26.

Answer 2

QUESTION:

• Find the ratio of (4x - 5y) & (5x + 2y) if (2x - y) : (2x + 4y) = 1:4

ANSWER:

Given:

• (2x - y) : (2x + 4y) = 1 : 4

To Find:

• (4x - 5y) : (5x + 2y)

Solution:

We are given that,

$\implies (2x - y) : (2x + 4y) = 1 : 4$

So,

$\implies \dfrac{2x - y}{2x + 4y} = \dfrac{1}{4}$

On cross multiplying,

$\implies 4(2x-y)=1(2x+4y)$

$\implies 4\!\!\!/^{\:2}(2x-y)=2\!\!\!/(x+2y)$

So,

$\implies 2(2x-y)=x+2y$

Solving the brackets,

$\implies 4x-2y=x+2y$

Transposing x to LHS,

$\implies 4x-2y-x=2y$

So,

$\implies 3x-2y=2y$

Transposing -2y to RHS,

$\implies 3x=2y+2y$

So,

$\implies 3x=4y$

Transposing 3 to RHS,

$\implies x=\dfrac{4}{3}y - - - -(1)$

Now, we need to find the value of,

$\implies (4x - 5y) : (5x + 2y)$

So,

$\implies \dfrac{4x - 5y}{5x + 2y}$

Substituting value of x from (1),

$\implies \dfrac{4x - 5y}{5x + 2y}$

$\implies \dfrac{4\left(\frac{4y}{3}\right) - 5y}{5\left(\frac{4y}{3}\right) + 2y}$

So,

$\implies \dfrac{\frac{16y}{3}- 5y}{\frac{20y}{3}+ 2y}$

Taking LCM,

$\implies \dfrac{\left(\frac{16y-15y}{3}\right)}{\left(\frac{20y+6y}{3}\right)}$

So,

$\implies \dfrac{\left(\frac{y}{3}\right)}{\left(\frac{26y}{3}\right)}$

Canceling 3,

$\implies \dfrac{\left(\frac{y}{3\!\!\!/}\right)}{\left(\frac{26y}{3\!\!\!/}\right)}$

So,

$\implies \dfrac{y}{26y}$

Canceling y,

$\implies \dfrac{1}{26}$

So,

$\implies 1:26$

Therefore,

$\implies\bf (4x - 5y) : (5x + 2y) = 1 : 26$