If x :y=3 :4, (4x+3y):(4y-4x)= ?

Correct option is B

Solution:

We are given that x : y = 3 : 4

which implies that $$\frac{x}{y} = \frac{3}{4}$$​ .

Let’s express x in terms of y :

x =$$\frac{3}{4}y$$​​

Now substitute this value of x into the given expression for the ratio

​$$\frac{4x + 3y}{4y - 4x}$$​​

​$$\frac{4x + 3y}{4y - 4x} = \frac{4\left( \frac{3}{4}y \right) + 3y}{4y - 4\left( \frac{3}{4}y \right)}$$​​

Simplifying both the numerator and denominator:

Numerator:

​$$4\left( \frac{3}{4}y \right) + 3y = 3y + 3y = 6y$$​​

Denominator:

​$$4y - 4\left( \frac{3}{4}y \right) = 4y - 3y = y$$​​

Thus, the ratio becomes:

​$$\frac{6y}{y} = 6$$:1​

Therefore, the value of $$\frac{4x + 3y}{4y - 4x}$$​ is 6:1.