In an office, the number of persons who take tea is twice the number of persons who take only coffee. The number of persons who take coffee is twice the number of persons who take only tea. Consider the following statements: 1. The number of persons taking either tea or coffee or both is 4 times those taking both tea and coffee. 2. The number of persons taking only coffee plus only tea is twice the number of those taking both. Which of the statements given above is/are correct?

Let's denote: OT = Number of persons who take only tea OC = Number of persons who take only coffee B = Number of persons who take both tea and coffee From the problem statement: 1. The number of persons who take tea (T) is twice the number of persons who take only coffee (OC). T = OT + B So, OT + B = 2 * OC (Equation 1) 2. The number of persons who take coffee (C) is twice the number of persons who take only tea (OT). C = OC + B So, OC + B = 2 * OT (Equation 2) Now, let's solve these two equations: Subtract Equation 2 from Equation 1: (OT + B) - (OC + B) = 2 * OC - 2 * OT OT - OC = 2 * OC - 2 * OT 3 * OT = 3 * OC Therefore, OT = OC Substitute OT = OC into Equation 1 (or Equation 2): OT + B = 2 * OT B = OT So, we have established the relationship: OT = OC = B. Let's represent this common value as 'x'. Thus, OT = x, OC = x, B = x. Now, let's evaluate the given statements: Statement 1: "The number of persons taking either tea or coffee or both is 4 times those taking both tea and coffee." The number of persons taking either tea or coffee or both (Union) = OT + OC + B Substitute our findings: Union = x + x + x = 3x The number of persons taking both tea and coffee = B = x Is 3x = 4 * x? No, this is incorrect (unless x=0, which would mean no one takes anything, making the ratios meaningless). So, Statement 1 is incorrect. The number is 3 times those taking both, not 4 times. Statement 2: "The number of persons taking only coffee plus only tea is twice the number of those taking both." Number taking only coffee plus only tea = OC + OT Substitute our findings: OC + OT = x + x = 2x The number of persons taking both = B = x Is 2x = 2 * x? Yes, this is correct. So, Statement 2 is correct. Based on the analysis, only Statement 2 is correct. The final answer is B) 2 only.