If x: y = 3:5, then what is the value of (2x + 5y): (2y – Зх)?

If x: y = 3:5, then what is the value of (2x + 5y): (2y – Зх)?

(A) 31: 1 (B) 19: 1 (C) 19: 6 (D) 31: 5

Given \(x: y = 3: 5\), we can express \(x\) and \(y\) in terms of a common factor. Let \(k\) be the common factor:

\[x = 3k\]
\[y = 5k\]

Now, substitute these values into the expression \((2x + 5y):(2y – 3x)\):

\[\frac{2(3k) + 5(5k)}{2(5k) – 3(3k)}\]

Simplify the expression:

\[\frac{6k + 25k}{10k – 9k}\]

\[\frac{31k}{k}\]

Cancel out the common factor \(k\):

\[31:1\]

So, the correct answer is (A) 31:1.

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