Question

If x:y=2:3, the value of (3x+2y):(2x+5y) is:

• A. \(\frac{12}{25}\)
• B. \(\frac{11}{27}\)
• C. \(\frac{11}{15}\)
• D. \(\frac{12}{19}\)

Answer 1

The Correct Option is D

To find the value of the ratio \((3x + 2y) : (2x + 5y)\) given that \(x : y = 2 : 3\), we can follow these steps:

1. From the given ratio \(x : y = 2 : 3\), we can express \(x\) and \(y\) in terms of a common variable, say \(k\). Thus, let \(x = 2k\) and \(y = 3k\).

2. Substitute these values into the expression \((3x + 2y)\).

   \[ 3x + 2y = 3(2k) + 2(3k) = 6k + 6k = 12k \]

3. Substitute \(x = 2k\) and \(y = 3k\) into the expression \((2x + 5y)\).

   \[ 2x + 5y = 2(2k) + 5(3k) = 4k + 15k = 19k \]

4. Now, the ratio \((3x + 2y) : (2x + 5y)\) becomes:

   \[ \frac{3x + 2y}{2x + 5y} = \frac{12k}{19k} = \frac{12}{19} \]

5. The final ratio \(\frac{12}{19}\) matches with option \(\frac{12}{19}\), thus confirming the correct answer.

Therefore, the value of \((3x + 2y) : (2x + 5y)\) is \(\frac{12}{19}\).