Question

Find the ratio of (4x - 5y) and (5x + 2y), if (2x - y): (2x + 4y) = 1:4?
a.3/26
b.7/17
c.1/26
d.21/7​

Answer 1

Answer:

find the find the ratio of 4 x minus 5 y and 5 x + 2 y if 2 x minus y ratio 2 x + 4 y is equal to 1 ratio 4?

Answer 2

Answer:

The correct answer is option c. $\frac{1}{26}$.

Step-by-step explanation:

Concept:

A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. The relationship between the amounts of two or more objects—referred to as a ratio—indicates how much of one object is contained in the other. The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as $a:b = \frac{a}{b}$ for any two quantities.

Given:

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

To find:

We have to find the ratio of $(4x - 5y)$ and $(5x + 2y)$.

Solution:

It is given that,

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

So,

$\frac{(2x - y)}{(2x + 4y)} =\frac{1}{4}$

By using cross multiply,

$4(2x - y)=1(2x+4y)\\8x-4y=2x+4y\\8x-2x=4y+4y\\6x=8y\\\frac{x}{y} =\frac{8}{6}\\\frac{x}{y} =\frac{4}{3}$

Now, put $\frac{x}{y} =\frac{4}{3}$ value in $(4x - 5y)$ and $(5x + 2y)$, as we have to find their ratio.

$=\frac{(4x - 5y)}{(5x + 2y)}$

$=\frac{(4\frac{x}{y} - 5)}{(5\frac{x}{y} + 2)}\\=\frac{(4(\frac{4}{3}) - 5)}{(5(\frac{4}{3}) + 2)}$

$=\frac{(\frac{16}{3} - 5)}{(\frac{20}{3} + 2)}\\=\frac{(\frac{16-15}{3})}{(\frac{20+6}{3})}$

$=\frac{\frac{1}{3}}{\frac{26}{3}}\\=\frac{1}{26}$

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