Calculating Unsold Model E Mobile Phones

This problem requires us to calculate the total number of Model E Mobile phones produced by the company in 2021 and 2022 combined, and then determine how many of these were left unsold based on the given sales percentage.

Understanding the Data

We are given the total production of Mobile Phones for two years and the percentage distribution of different models for each year. We also know the overall percentage of Model E phones sold across these two years.

• Total Mobile Phones produced in 2021: 4,50,000
• Total Mobile Phones produced in 2022: 5,20,000
• Percentage of Model E sold (2021 & 2022): 85%

Step-by-Step Calculation of Unsold Model E Phones

1. Calculate Model E Production in 2021

The production of Model E Mobile phones in 2021 is 20% of the total production in 2021.

Production of Model E in 2021 = $4,50,000 \times 20\% = 4,50,000 \times \frac{20}{100} = 4,50,000 \times 0.20$

Production of Model E in 2021 = $90,000$ Mobile phones.

2. Calculate Model E Production in 2022

The production of Model E Mobile phones in 2022 is 10% of the total production in 2022.

Production of Model E in 2022 = $5,20,000 \times 10\% = 5,20,000 \times \frac{10}{100} = 5,20,000 \times 0.10$

Production of Model E in 2022 = $52,000$ Mobile phones.

3. Calculate Total Model E Production (2021 & 2022)

The total number of Model E Mobile phones produced over the two years is the sum of production in 2021 and 2022.

Total Model E Production = Production in 2021 + Production in 2022

Total Model E Production = $90,000 + 52,000 = 142,000$ Mobile phones.

4. Calculate the Percentage of Unsold Model E Phones

If 85% of the Model E phones produced were sold, the remaining percentage was unsold.

Percentage Unsold = 100% - Percentage Sold

Percentage Unsold = $100\% - 85\% = 15\%$

5. Calculate the Number of Unsold Model E Phones

The number of unsold Model E Mobile phones is 15% of the total Model E phones produced over the two years.

Number of Unsold Model E Phones = Total Model E Production $\times$ Percentage Unsold

Number of Unsold Model E Phones = $142,000 \times 15\% = 142,000 \times \frac{15}{100} = 142,000 \times 0.15$

Number of Unsold Model E Phones = $1420 \times 15$

To calculate $1420 \times 15$: $1420 \times (10 + 5) = (1420 \times 10) + (1420 \times 5) = 14200 + 7100 = 21300$

Therefore, $21,300$ Model E Mobile phones were left unsold by the company.

Summary of Calculation

Here is a quick summary of the steps:

1. Calculate Model E production in 2021: $4,50,000 \times 0.20 = 90,000$.
2. Calculate Model E production in 2022: $5,20,000 \times 0.10 = 52,000$.
3. Find total Model E production: $90,000 + 52,000 = 142,000$.
4. Calculate the unsold percentage: $100\% - 85\% = 15\%$.
5. Calculate the number of unsold Model E phones: $142,000 \times 0.15 = 21,300$.

The number of Model E Mobile phones left unsold is 21,300.

Revision Table: Mobile Phone Production and Sales

Additional Information: Data Interpretation Basics

Interpreting data from tables is a common skill required in many exams. Here are some basic points to remember:

• Percentages: Percentages represent a part out of a hundred. To convert a percentage to a decimal, divide by 100 (e.g., 20% = 0.20).
• Calculating Value from Percentage: To find the actual value represented by a percentage, multiply the total value by the percentage (in decimal form). For example, 20% of 4,50,000 is $4,50,000 \times 0.20$.
• Combining Data: When calculating totals or differences across categories or time periods, make sure to sum or subtract the absolute values, not just the percentages.
• Understanding "Unsold": If a certain percentage is sold, the remaining percentage is unsold. The unsold quantity is calculated based on the total quantity produced.

These fundamental concepts help in accurately analysing data presented in tables or charts, like the one showing mobile phone production and sales data.