Question

a:b=5:3 then (8a-5b): (8a+5b) is equal to​

Answer 1

For the given ratio a:b = 5:3, the value of (8a-5b): (8a+5b) is equal to 5:11.

Given,

Ratio, a:b = 5:3.

To find,

Ratio:

(8a-5b): (8a+5b).

Solution,

It can be seen here that, the ratio of a and b is given to be 5:3, such that

$\frac{a}{b} =\frac{5}{3}$

Let the values of a and b be as follows.

a = 5x, and

b = 3x.

We have to determine the ratio $\frac{8a-5b}{8a+5b}.$

Substituting the values of a and b from above, we get,

$\frac{8a-5b}{8a+5b}=\frac{8(5x)-5(3x)}{8(5x)+5(3x)}$

$\implies \frac{8a-5b}{8a+5b}=\frac{40x-15x}{40x+15x}\\\implies \frac{8a-5b}{8a+5b}=\frac{25x}{55x}\\\implies \frac{8a-5b}{8a+5b}=\frac{25}{55}$

Further simplifying the above result,

$\frac{8a-5b}{8a+5b}=\frac{5}{11}.$

So, the value of (8a-5b): (8a+5b) is 5:11.

Therefore, for the given ratio a:b = 5:3, the value of (8a-5b): (8a+5b) is equal to 5:11.

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Answer 2

(8a-5b):(8a+5b) is 5:11

Given:

a:b=5:3

To Find:

(8a-5b):(8a+5b)

Solution:

$\frac{a}{b} = \frac{5}{3}$

Let, a= 5x and b= 3x

Putting the values in

$\frac{(8a-5b)}{(8a+5b)} = \frac{8(5x) - 5(3x)}{8(5x) + 5(3x)}$

⇒ $\frac{40x - 15x}{40x + 15x} = \frac{25x}{55x}$

⇒$\frac{5}{11}$

Therefore, (8a-5b):(8a+5b) is 5:11