Mobile Phone Production Data Analysis and Percentage Increase Calculation

The question asks us to analyze the mobile phone production data provided in the table for the years 2021 and 2022. We need to find the number of Model-B phones produced in 2022 and the number of Model-D phones produced in 2021, and then calculate the approximate percentage by which the number of Model-B in 2022 is more than the number of Model-D in 2021.

First, let's look at the given data:

• Total production in 2021: 4,50,000 mobile phones.
• Total production in 2022: 5,20,000 mobile phones.
• The table shows the percentage distribution of different models (A, B, C, D, E) for each year.

Calculating the Number of Phones for Specific Models

We need to find the actual number of Model-B phones produced in 2022 and Model-D phones produced in 2021.

Number of Model-B phones in 2022:

From the table, Model-B production was 30% of the total production in 2022.

\(\text{Number of Model-B in 2022} = 30\% \text{ of Total Production in 2022}\)

\(\text{Number of Model-B in 2022} = \frac{30}{100} \times 5,20,000\)

\(\text{Number of Model-B in 2022} = 0.30 \times 5,20,000 = 1,56,000\)

Number of Model-D phones in 2021:

From the table, Model-D production was 10% of the total production in 2021.

\(\text{Number of Model-D in 2021} = 10\% \text{ of Total Production in 2021}\)

\(\text{Number of Model-D in 2021} = \frac{10}{100} \times 4,50,000\)

\(\text{Number of Model-D in 2021} = 0.10 \times 4,50,000 = 45,000\)

Calculating the Percentage Increase

Now we need to find out by what percentage the number of Model-B phones in 2022 (1,56,000) is more than the number of Model-D phones in 2021 (45,000). The formula for percentage increase is:

\(\text{Percentage Increase} = \frac{\text{Change in Value}}{\text{Original Value}} \times 100\)

Here, the 'Change in Value' is the difference between the number of Model-B in 2022 and Model-D in 2021, and the 'Original Value' is the number of Model-D in 2021.

Change in Value \( = \text{Number of Model-B in 2022} - \text{Number of Model-D in 2021}\)

Change in Value \( = 1,56,000 - 45,000 = 1,11,000\)

Percentage Increase \( = \frac{1,11,000}{45,000} \times 100\)

We can simplify the fraction:

\(\text{Percentage Increase} = \frac{111}{45} \times 100\)

Both 111 and 45 are divisible by 3:

\(\text{Percentage Increase} = \frac{111 \div 3}{45 \div 3} \times 100 = \frac{37}{15} \times 100\)

\(\text{Percentage Increase} = \frac{3700}{15}\)

Performing the division:

\(\frac{3700}{15} = \frac{740}{3} \approx 246.66...\)

The question asks for the approximate percentage. Rounding 246.66... to the nearest integer gives 247%.

Therefore, the number of Mobile phones of Model-B in the year 2022 is approximately 247% more than the number of Model-D Mobile phones in the year 2021.

Revision Table: Key Data Points and Calculations

Here is a summary of the key numbers used in solving this problem:

Additional Information: Percentage Concepts in Data Analysis

Understanding percentages is crucial for interpreting data presented in tables and charts. A percentage represents a part out of a hundred. In this problem, we used percentages to find the actual number of items from a total and to calculate a percentage increase.

Calculating a Percentage of a Total:

To find \(X\%\) of a total value \(T\), you calculate \(\frac{X}{100} \times T\). This was used to find the number of specific phone models.

Calculating Percentage Increase:

Percentage increase measures how much a value has increased in relation to its original value. The formula is \(\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\). In our case, the 'Original Value' was the number of Model-D phones in 2021, and the 'New Value' was the number of Model-B phones in 2022. The increase is relative to the base value, which is the number we are comparing against (Model-D in 2021).

Percentage increase problems often involve comparing quantities from different categories or time periods, as seen in this mobile phone production data analysis question.