Analyzing Newspaper Data and Ratios

This question asks for the ratio of the total number of distributed newspapers to the total number of newspapers printed based on the data provided in the table.

Understanding the Newspaper Data Table

The table gives us two key pieces of information for several newspapers (A, B, C, D) across different cities (Delhi, Lucknow, Varanasi, Jaipur):

• The total number of copies printed for each newspaper (shown in brackets next to the newspaper name).
• The number of copies of each newspaper distributed in each city.

We need to sum up the total printed newspapers and the total distributed newspapers from all cities and all newspapers to find the required ratio.

Calculating Total Newspapers Printed

The total number of newspapers printed is the sum of the quantities printed for each newspaper type (A, B, C, and D). These numbers are given in brackets next to the newspaper names.

Total Printed Newspapers \( = \) Newspaper A Printed \( + \) Newspaper B Printed \( + \) Newspaper C Printed \( + \) Newspaper D Printed

Total Printed Newspapers \( = 2000 + 2000 + 1000 + 1000 = 6000\)

Calculating Total Newspapers Distributed

The total number of newspapers distributed is the sum of all the distributed quantities for all newspapers across all cities.

We can calculate the total distributed per city or sum up all entries directly. Let's sum by city for clarity:

• Total Distributed in Delhi \( = 1000 + 750 + 320 + 250 = 2320\)
• Total Distributed in Lucknow \( = 500 + 250 + 250 + 175 = 1175\)
• Total Distributed in Varanasi \( = 200 + 150 + 165 + 155 = 670\)
• Total Distributed in Jaipur \( = 200 + 350 + 135 + 160 = 845\)

Now, sum the totals from each city to get the overall total distributed newspapers:

Total Distributed Newspapers \( = \) Total in Delhi \( + \) Total in Lucknow \( + \) Total in Varanasi \( + \) Total in Jaipur

Total Distributed Newspapers \( = 2320 + 1175 + 670 + 845 = 5010\)

Finding the Ratio of Distributed to Printed Newspapers

The question asks for the ratio of total distributed newspaper to total newspaper printed.

Ratio \( = \) Total Distributed Newspapers : Total Printed Newspapers

Ratio \( = 5010 : 6000\)

To simplify the ratio, we can divide both numbers by their greatest common divisor. First, divide by 10:

\( \frac{5010}{10} : \frac{6000}{10} = 501 : 600\)

Now, check for other common factors. Both 501 and 600 are divisible by 3 (sum of digits of 501 is \(5+0+1=6\), divisible by 3; sum of digits of 600 is \(6+0+0=6\), divisible by 3).

\( \frac{501}{3} : \frac{600}{3} = 167 : 200\)

The numbers 167 and 200 do not have common factors greater than 1 (167 is a prime number). Therefore, the simplified ratio is \(167 : 200\).

Conclusion on the Newspaper Ratio

Based on the calculations from the newspaper data table, the ratio of total distributed newspapers to total printed newspapers is \(167 : 200\).

Revision Table: Key Calculations for Newspaper Data

Additional Information on Ratios and Data Interpretation

Understanding ratios is fundamental in data interpretation. A ratio compares two quantities. In this case, we compared the quantity of distributed newspapers to the quantity of printed newspapers.

• Ratio Definition: A ratio is a way to compare two or more quantities. It can be written as \(a:b\) or \(\frac{a}{b}\).
• Simplifying Ratios: Ratios are usually expressed in their simplest form by dividing both parts by their greatest common divisor (GCD). This is similar to simplifying fractions.
• Data Interpretation: This question is an example of data interpretation from a table. It requires extracting relevant numbers, performing calculations (addition), and then simplifying the resulting ratio. Always read the question carefully to identify which quantities need to be compared and in which order (e.g., distributed to printed, not printed to distributed).

Practice with different types of tables and charts helps improve data interpretation skills, which are important for various exams.