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Table with Missing Values
A company manufactures four types of products: A, B, C, and D. The table below presents the percentage distribution of sales (in terms of units) across four quarters (Q1, Q2, Q3, Q4) for each product. Some values are missing. The 'Total Sales (Units)' column indicates the total sales for each product over the entire year. The 'Total Units Sold in Quarter' row indicates the sum of units sold for all products in that specific quarter. It is given that the sum of the percentage sales for each product across the four quarters is 100%. $$\begin{array}{|c|c|c|c|c|c|}\hline \textbf{Product / Quarter} & \textbf{Q1} & \textbf{Q2} & \textbf{Q3} & \textbf{Q4} & \textbf{Total Sales (Units)}\\ \hline \textbf{A} & 20\% & 25\% & \text{X}\% & 30\% & 8000 \\ \hline \textbf{B} & 15\% & \text{Y}\% & 30\% & 20\% & 12000 \\ \hline \textbf{C} & 25\% & 20\% & 35\% & \text{Z}\% & 10000 \\ \hline \textbf{D} & 30\% & 20\% & 25\% & 25\% & \text{P} \\ \hline \textbf{Total Units Sold in Quarter} & 8400 & 10000 & 11000 & 10500 & \text{T} \\ \hline \end{array}$$ Based on the information provided, what is the sales quantity (in units) of Product D in Quarter 2 (Q2)? A) 1600 B) 1800 C) 2000 D) 2500
The correct answer is **B) 1800**. Here is a detailed, step-by-step solution: **Step 1: Determine the missing percentage values (X, Y, Z) for Products A, B, and C.** As per the given information, the sum of percentage sales for each product across the four quarters must be 100%. * **For Product A:** $20\% + 25\% + \text{X}\% + 30\% = 100\%$ $75\% + \text{X}\% = 100\%$ $\text{X}\% = 100\% - 75\% = 25\%$ So, $\text{X} = 25$. * **For Product B:** $15\% + \text{Y}\% + 30\% + 20\% = 100\%$ $65\% + \text{Y}\% = 100\%$ $\text{Y}\% = 100\% - 65\% = 35\%$ So, $\text{Y} = 35$. * **For Product C:** $25\% + 20\% + 35\% + \text{Z}\% = 100\%$ $80\% + \text{Z}\% = 100\%$ $\text{Z}\% = 100\% - 80\% = 20\%$ So, $\text{Z} = 20$. **Step 2: Calculate the unit sales for Products A, B, and C in Quarter 2 (Q2).** To find the actual unit sales, multiply the product's total annual sales by its respective percentage for Q2. * **Sales of Product A in Q2:** Product A's sales in Q2 are 25% (the calculated value of X) of its total annual sales (8000 units). $\text{Units (A, Q2)} = 25\% \text{ of } 8000 = \frac{25}{100} \times 8000 = 2000 \text{ units}$. * **Sales of Product B in Q2:** Product B's sales in Q2 are 35% (the calculated value of Y) of its total annual sales (12000 units). $\text{Units (B, Q2)} = 35\% \text{ of } 12000 = \frac{35}{100} \times 12000 = 4200 \text{ units}$. * **Sales of Product C in Q2:** Product C's sales in Q2 are 20% of its total annual sales (10000 units). $\text{Units (C, Q2)} = 20\% \text{ of } 10000 = \frac{20}{100} \times 10000 = 2000 \text{ units}$. **Step 3: Calculate the sales quantity of Product D in Quarter 2 (Q2).** The 'Total Units Sold in Quarter' row provides the sum of sales for all products in a given quarter. For Q2, this total is 10000 units. Let $\text{Units (D, Q2)}$ be the sales quantity of Product D in Q2. The sum of unit sales for all products in Q2 must equal the total units sold in Q2: $\text{Units (A, Q2)} + \text{Units (B, Q2)} + \text{Units (C, Q2)} + \text{Units (D, Q2)} = \text{Total Units Sold in Q2}$ Substitute the calculated values: $2000 + 4200 + 2000 + \text{Units (D, Q2)} = 10000$ Combine the known values: $8200 + \text{Units (D, Q2)} = 10000$ Solve for $\text{Units (D, Q2)}$: $\text{Units (D, Q2)} = 10000 - 8200 = 1800 \text{ units}$. Thus, the sales quantity of Product D in Quarter 2 is 1800 units. The final answer is $\boxed{1800}$.
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