Let A and B be two sets such that n(A – B) = 20 + x, n(B – A) = 3x and n(A∩B) = x + 1. If n(A) = n(B), then the value of (2x – 5) is:

Correct option is C

​$$\textbf{Given:} \\n(A - B) = 20 + x \\n(B - A) = 3x \\n(A \cap B) = x + 1 \\n(A) = n(B) \\\textbf{Concept Used:} \\\text{Number of elements in sets} \\\textbf{Formula Used:} \\n(A) = n(A - B) + n(A \cap B) \\n(B) = n(B - A) + n(A \cap B) \\\textbf{Solution:} \\n(A) = (20 + x) + (x + 1) \\n(A) = 21 + 2x \\n(B) = 3x + (x + 1) \\n(B) = 4x + 1 \\\text{Given } n(A) = n(B): \\21 + 2x = 4x + 1 \\21 - 1 = 4x - 2x \\20 = 2x \\x = 10 \\\text{Required value:} \\2x - 5 = 2(10) - 5 \\= 20 - 5 \\= 15 \\\textbf{Final Answer:} \\15$$​​