Understanding Mobile Phone Production Data

The question provides data on the percentage distribution of five different models (A, B, C, D, and E) of mobile phones produced by a company over two years, 2021 and 2022. The total number of mobile phones produced in each year is also given: 4,50,000 in 2021 and 5,20,000 in 2022. We need to use this information to calculate the ratio of the number of mobile phones of specific models from 2022 to specific models from 2021.

First, let's look at the provided data table showing the percentage distribution of mobile phone models:

Calculating Mobile Phones Produced in 2022

We need to find the number of mobile phones of Models C, D, and E produced in the year 2022. The total production in 2022 was 5,20,000 mobile phones.

• Percentage of Model C in 2022 = 25%
• Percentage of Model D in 2022 = 25%
• Percentage of Model E in 2022 = 10%

The combined percentage of Models C, D, and E in 2022 is:

$$(25\% + 25\% + 10\%) = 60\%$$

The number of mobile phones of Models C, D, and E in 2022 is:

$$\text{Number (C+D+E in 2022)} = \frac{60}{100} \times 5,20,000$$ $$\text{Number (C+D+E in 2022)} = 0.60 \times 5,20,000$$ $$\text{Number (C+D+E in 2022)} = 3,12,000$$

Calculating Mobile Phones Produced in 2021

Next, we need to find the number of mobile phones of Models B, C, and D produced in the year 2021. The total production in 2021 was 4,50,000 mobile phones.

• Percentage of Model B in 2021 = 25%
• Percentage of Model C in 2021 = 30%
• Percentage of Model D in 2021 = 10%

The combined percentage of Models B, C, and D in 2021 is:

$$(25\% + 30\% + 10\%) = 65\%$$

The number of mobile phones of Models B, C, and D in 2021 is:

$$\text{Number (B+C+D in 2021)} = \frac{65}{100} \times 4,50,000$$ $$\text{Number (B+C+D in 2021)} = 0.65 \times 4,50,000$$ $$\text{Number (B+C+D in 2021)} = 2,92,500$$

Determining the Required Ratio

The question asks for the ratio of the number of Mobile phones of Models C, D and E in the year 2022 to the number of Mobile phones of Models B, C and D in the year 2021.

$$\text{Ratio} = \frac{\text{Number (C+D+E in 2022)}}{\text{Number (B+C+D in 2021)}}$$ $$\text{Ratio} = \frac{3,12,000}{2,92,500}$$

To simplify the ratio, we can divide both the numerator and the denominator by common factors. First, divide by 1000:

$$\text{Ratio} = \frac{312}{292.5}$$

Multiply numerator and denominator by 10 to remove decimal:

$$\text{Ratio} = \frac{3120}{2925}$$

Now, let's find the greatest common divisor or divide by smaller common factors. Both numbers end in 0 or 5, so they are divisible by 5.

$$3120 \div 5 = 624$$ $$2925 \div 5 = 585$$ $$\text{Ratio} = \frac{624}{585}$$

Let's check if they are divisible by 3 (sum of digits: 6+2+4=12, divisible by 3; 5+8+5=18, divisible by 3).

$$624 \div 3 = 208$$ $$585 \div 3 = 195$$ $$\text{Ratio} = \frac{208}{195}$$

Let's check for common factors again. We can see that $208 = 16 \times 13$ and $195 = 15 \times 13$. Both are divisible by 13.

$$208 \div 13 = 16$$ $$195 \div 13 = 15$$ $$\text{Ratio} = \frac{16}{15}$$

The ratio is 16 : 15.

Summary of Calculation Steps

To find the ratio, we performed the following steps:

1. Identified the total production for each year (2021 and 2022).
2. Calculated the combined percentage of Models C, D, and E for the year 2022.
3. Calculated the number of mobile phones for Models C, D, and E in 2022 based on the total production and combined percentage.
4. Calculated the combined percentage of Models B, C, and D for the year 2021.
5. Calculated the number of mobile phones for Models B, C, and D in 2021 based on the total production and combined percentage.
6. Formed the ratio of the number of phones from 2022 to 2021.
7. Simplified the ratio to its lowest terms.

The number of Mobile phones of Models C, D, and E in 2022 is 3,12,000. The number of Mobile phones of Models B, C, and D in 2021 is 2,92,500. The ratio is $3,12,000 : 2,92,500$, which simplifies to $16 : 15$.

Revision Table: Key Calculations for Mobile Phone Production

Additional Information: Understanding Ratios in Data Analysis

Ratios are used to compare two or more quantities. In data analysis, calculating ratios helps us understand the proportional relationship between different parts of the data. A ratio like $16 : 15$ means that for every 16 units of the first quantity (Mobile phones C, D, E in 2022), there are 15 units of the second quantity (Mobile phones B, C, D in 2021).

To simplify a ratio of two numbers, you find the greatest common divisor (GCD) of the numbers and divide both numbers by the GCD. This gives the ratio in its simplest form. In our calculation, we found that 13 was a common factor after initial divisions by 5 and 3.

Data interpretation questions often require calculating percentages, totals, averages, and ratios based on tables, charts, or graphs. Understanding how to extract the correct data points and perform the necessary calculations is crucial. This question combined percentage calculations with ratio simplification.