Three resistors $$\text R_1,\text R_2$$​ and $$\text R_3$$​ have their resistance values in the ratio of 2 : 3 : 4. They are combined in parallel and their equivalent resistance is 24 Ω. Then the individual resistances $$\text R_1,\text R_2$$​ and $$\text R_3$$​ are:

Correct option is D

​$$\text{Given:} \\\text{The ratio of the resistances is } R_1 : R_2 : R_3 = 2 : 3 : 4. \\\text{The combined equivalent resistance of the three resistors in parallel is } 24 \ \Omega. \\\text{We are asked to find the individual resistances } R_1, R_2, R_3.$$

$$\text{Let the resistances be:} \\R_1 = 2x \\R_2 = 3x \\R_3 = 4x$$

$$\text{The formula for the equivalent resistance } R_{\text{eq}} \text{ of resistors in parallel is:} \\\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \\\text{Substitute the given values into the equation:} \\\frac{1}{24} = \frac{1}{2x} + \frac{1}{3x} + \frac{1}{4x}$$

$$\frac{1}{24} = \frac{1}{2x} + \frac{1}{3x} + \frac{1}{4x} = \frac{6 + 4 + 3}{12x} = \frac{13}{12x} \\\text{Now, solve for } x: \\\frac{1}{24} = \frac{13}{12x} \Rightarrow 12x = 13 \times 24 \\12x = 312 \Rightarrow x = 26$$

$$\text{Now that we know } x = 26, \text{ we can calculate the values of } R_1, R_2, R_3: \\R_1 = 2x = 2 \times 26 = 52 \, \Omega \\R_2 = 3x = 3 \times 26 = 78 \, \Omega \\R_3 = 4x = 4 \times 26 = 104 \, \Omega$$​​​​​​