Correct Answer: B) 300 Let's denote the missing values in the table for clarity: $Y_A$ = Sales of Product Y by Department A $X_B$ = Sales of Product X by Department B $Z_B$ = Sales of Product Z by Department B $T_B$ = Total Sales by Department B $T_C$ = Total Sales by Department C $T_Y$ = Total Sales of Product Y across all departments $T_Z$ = Total Sales of Product Z across all departments $T_{Grand}$ = Grand Total Sales The initial table with explicit missing values: $$ \begin{array}{|l|c|c|c|c|} \hline \textbf{Department} & \textbf{Product X} & \textbf{Product Y} & \textbf{Product Z} & \textbf{Total Sales} \\ \hline \text{A} & 120 & Y_A & 80 & 300 \\ \text{B} & X_B & 90 & Z_B & T_B \\ \text{C} & 100 & 110 & 70 & T_C \\ \hline \textbf{Total} & 350 & T_Y & T_Z & T_{Grand} \\ \hline \end{array} $$ We will fill the table step-by-step using the principle of arithmetic consistency (sum of values in a row equals the row total, and sum of values in a column equals the column total). **Step 1: Calculate $Y_A$ (Sales of Product Y by Department A)** For Department A, the sum of sales of products X, Y, and Z must equal its total sales. $120 + Y_A + 80 = 300$ $200 + Y_A = 300$ $Y_A = 300 - 200 = 100$ units. **Step 2: Calculate $T_C$ (Total Sales by Department C)** For Department C, the sum of sales of products X, Y, and Z must equal its total sales. $T_C = 100 + 110 + 70 = 280$ units. **Step 3: Calculate $X_B$ (Sales of Product X by Department B)** For Product X, the sum of sales from departments A, B, and C must equal the total sales of Product X. $120 + X_B + 100 = 350$ $220 + X_B = 350$ $X_B = 350 - 220 = 130$ units. At this point, the table (with known values filled) looks like: $$ \begin{array}{|l|c|c|c|c|} \hline \textbf{Department} & \textbf{Product X} & \textbf{Product Y} & \textbf{Product Z} & \textbf{Total Sales} \\ \hline \text{A} & 120 & 100 & 80 & 300 \\ \text{B} & 130 & 90 & Z_B & T_B \\ \text{C} & 100 & 110 & 70 & 280 \\ \hline \textbf{Total} & 350 & T_Y & T_Z & T_{Grand} \\ \hline \end{array} $$ **Step 4: Use the given constraint to find $T_B$ (Total Sales by Department B)** The problem states: "The total sales of Department B is equal to the total sales of Department C." From Step 2, we found $T_C = 280$ units. Therefore, $T_B = 280$ units. **Step 5: Calculate $Z_B$ (Sales of Product Z by Department B)** For Department B, the sum of sales of products X, Y, and Z must equal its total sales. $X_B + 90 + Z_B = T_B$ From Step 3, $X_B = 130$. From Step 4, $T_B = 280$. $130 + 90 + Z_B = 280$ $220 + Z_B = 280$ $Z_B = 280 - 220 = 60$ units. Now, we have all the values required to calculate the total sales of Product Y. The relevant portions of the table are: $$ \begin{array}{|l|c|c|c|c|} \hline \textbf{Department} & \textbf{Product X} & \textbf{Product Y} & \textbf{Product Z} & \textbf{Total Sales} \\ \hline \text{A} & 120 & 100 & 80 & 300 \\ \text{B} & 130 & 90 & 60 & 280 \\ \text{C} & 100 & 110 & 70 & 280 \\ \hline \textbf{Total} & 350 & T_Y & T_Z & T_{Grand} \\ \hline \end{array} $$ **Step 6: Calculate $T_Y$ (Total Sales of Product Y across all departments)** The total sales of Product Y is the sum of sales of Product Y from departments A, B, and C. $T_Y = Y_A + 90 + 110$ From Step 1, $Y_A = 100$. $T_Y = 100 + 90 + 110$ $T_Y = 300$ units. Thus, the total sales of Product Y across all departments is 300 units.