If mean of the following distribution is 211, then what is the value of (4p – 3q)?

Correct option is B

​$$\textbf{Given:} \\\text{Mean} = 211 \\\text{Total frequency} = 25 \\\textbf{Concept Used:} \\\text{Mean of grouped data} \\\textbf{Formula Used:} \\\text{Mean} = \frac{\sum fx}{\sum f} \\\textbf{Solution:} \\\text{Mid-points} = 125,\,175,\,225,\,275,\,325 \\4 + p + 12 + q + 2 = 25 \\p + q = 7 \\\sum fx = 211 \times 25 = 5275 \\4(125) + 12(225) + 2(325) = 3850 \\3850 + 175p + 275q = 5275 \\175p + 275q = 1425 \\7p + 11q = 57 \\p = 7 - q \\7(7 - q) + 11q = 57 \\49 - 7q + 11q = 57 \\4q = 8 \\q = 2 \\p = 5 \\4p - 3q = 4(5) - 3(2) = 14 \\\textbf{Final Answer:} \\14$$​​