Understanding the Item Production Data Table

The provided data table shows the percentage distribution of six different types of items (A, B, C, D, E, F) produced by a company over two years, 2020 and 2021. We are also given the total number of items produced in each of these years. This type of question requires careful data interpretation and calculation based on percentages.

Total production in 2020 = 48600 items

Total production in 2021 = 62500 items

Question Asked: Total Production of Items A, B, C

The question asks for the combined total number of items of type A, type B, and type C produced by the company in both 2020 and 2021.

Step-by-Step Calculation of Item Production

To find the total number of items of types A, B, and C produced together across both years, we need to calculate the number of items for each type in each year and then sum them up.

Calculating Production in 2020

The total production in 2020 was 48600 items. We use the percentages for 2020 to find the count for each item type.

• Number of items of type A in 2020:

  \( \text{Items A in 2020} = \text{Total Production in 2020} \times \frac{\text{\% Distribution of A in 2020}}{100} \)

  \( \text{Items A in 2020} = 48600 \times \frac{17}{100} \)

  \( \text{Items A in 2020} = 486 \times 17 = 8262 \)

• Number of items of type B in 2020:

  \( \text{Items B in 2020} = \text{Total Production in 2020} \times \frac{\text{\% Distribution of B in 2020}}{100} \)

  \( \text{Items B in 2020} = 48600 \times \frac{18}{100} \)

  \( \text{Items B in 2020} = 486 \times 18 = 8748 \)

• Number of items of type C in 2020:

  \( \text{Items C in 2020} = \text{Total Production in 2020} \times \frac{\text{\% Distribution of C in 2020}}{100} \)

  \( \text{Items C in 2020} = 48600 \times \frac{17}{100} \)

  \( \text{Items C in 2020} = 486 \times 17 = 8262 \)

Total items of type A, B, and C produced in 2020 = \( 8262 + 8748 + 8262 = 25272 \)

Calculating Production in 2021

The total production in 2021 was 62500 items. We use the percentages for 2021 to find the count for each item type.

• Number of items of type A in 2021:

  \( \text{Items A in 2021} = \text{Total Production in 2021} \times \frac{\text{\% Distribution of A in 2021}}{100} \)

  \( \text{Items A in 2021} = 62500 \times \frac{18}{100} \)

  \( \text{Items A in 2021} = 625 \times 18 = 11250 \)

• Number of items of type B in 2021:

  \( \text{Items B in 2021} = \text{Total Production in 2021} \times \frac{\text{\% Distribution of B in 2021}}{100} \)

  \( \text{Items B in 2021} = 62500 \times \frac{15}{100} \)

  \( \text{Items B in 2021} = 625 \times 15 = 9375 \)

• Number of items of type C in 2021:

  \( \text{Items C in 2021} = \text{Total Production in 2021} \times \frac{\text{\% Distribution of C in 2021}}{100} \)

  \( \text{Items C in 2021} = 62500 \times \frac{8}{100} \)

  \( \text{Items C in 2021} = 625 \times 8 = 5000 \)

Total items of type A, B, and C produced in 2021 = \( 11250 + 9375 + 5000 = 25625 \)

Calculating Total Production of A, B, C in 2020 and 2021

To find the total number of items of type A, B, and C produced in both years combined, we add the totals from 2020 and 2021.

\( \text{Total A+B+C (2020 & 2021)} = \text{Total A+B+C (2020)} + \text{Total A+B+C (2021)} \)

\( \text{Total A+B+C (2020 & 2021)} = 25272 + 25625 \)

\( \text{Total A+B+C (2020 & 2021)} = 50897 \)

Final Answer Determination

The total number of items of type A, B, and C produced by the company in 2020 and 2021 together is 50897.

Revision Table: Key Data Points and Calculations

Grand Total (A+B+C in 2020 and 2021) = \( 25272 + 25625 = 50897 \)

Additional Information on Percentage Distribution

Percentage distribution tables like this are common in data interpretation questions. They show how a total quantity is divided among different categories. To find the actual number or value for a category, you multiply the total by the category's percentage and divide by 100. This skill is fundamental for solving problems based on surveys, production data, sales figures, etc.

• Percentage means 'out of one hundred'. So, 17% is equivalent to \( \frac{17}{100} \).
• To find 'X% of a Total', the formula is \( \frac{X}{100} \times \text{Total} \).
• When combining data from multiple years or categories, calculate the specific values for each part first, then add them up as required by the question.