Understanding the Data and the Goal

The question asks us to calculate the total percentage of literates across four different cities: A, B, C, and D. We are provided with a table containing data about the population, number of literates, number of illiterates, and percentage of literates for each city. However, some values are missing. To find the total percentage of literates, we first need to find the total population and the total number of literates across all cities. This requires us to fill in the missing values in the table.

Finding Missing City Population Data

We can find the missing values by using the relationship between population, literates, and illiterates:

• Population = Literate + Illiterate
• % of Literates = $(\frac{\text{Literate}}{\text{Population}}) \times 100$
• % of Illiterates = $(\frac{\text{Illiterate}}{\text{Population}}) \times 100$
• % of Literates + % of Illiterates = 100%

Let's find the missing values for each city:

• City A: Population = 200, Literate = 150, Illiterate = 50. The percentage of literates is missing. Percentage of Literates in City A = $(\frac{\text{Literate}}{\text{Population}}) \times 100 = (\frac{150}{200}) \times 100 = 0.75 \times 100 = 75\%$
• City B: Literate = 200, Illiterate = 100. Population is missing. Population of City B = Literate + Illiterate = $200 + 100 = 300$. The percentage of literates is given as 66.6%. Let's check: $(\frac{200}{300}) \times 100 = 66.66...\%$, which is approximately 66.6%. This confirms our population calculation.
• City C: Population = 150, Literate = 50, Illiterate = 100. The percentage of literates is missing. Percentage of Literates in City C = $(\frac{\text{Literate}}{\text{Population}}) \times 100 = (\frac{50}{150}) \times 100 = \frac{1}{3} \times 100 = 33.33...\%$
• City D: Population = 120, Illiterate = 90. Literate is missing. Also, the percentage of literates is given as 25%. We can find the number of literates in two ways: Method 1: Literate = Population - Illiterate = $120 - 90 = 30$. Method 2: Using the percentage of literates: Literate = $(\frac{\text{% of Literates}}{100}) \times \text{Population} = (\frac{25}{100}) \times 120 = 0.25 \times 120 = 30$. Both methods give the same result. The number of literates in City D is 30.

Now we have the complete data for all cities:

Calculating Total Population and Total Literates

To find the total percentage of literates across the four cities combined, we need the sum of the populations and the sum of the literate individuals from all cities.

• Total Population = Population(A) + Population(B) + Population(C) + Population(D) Total Population = $200 + 300 + 150 + 120 = 770$
• Total Literate Individuals = Literate(A) + Literate(B) + Literate(C) + Literate(D) Total Literate Individuals = $150 + 200 + 50 + 30 = 430$

Calculating the Total Percentage of Literates

Now we can calculate the overall percentage of literates for all four cities combined using the total figures:

Total Percentage of Literates = $(\frac{\text{Total Literate Individuals}}{\text{Total Population}}) \times 100$

Total Percentage of Literates = $(\frac{430}{770}) \times 100$

Let's perform the calculation:

$\frac{430}{770} \approx 0.5584415...$

Multiply by 100:

$0.5584415... \times 100 \approx 55.84415...$

Rounding the Result

The question asks us to round the result to one decimal place. The first decimal place is 8. The second decimal place is 4. Since 4 is less than 5, we round down, keeping the first decimal place as it is.

Rounded Percentage = $55.8\%$

Therefore, the total percentage of literates in the four cities together, rounded to one decimal place, is 55.8%.

Revision Table: Key Calculations

Additional Information on Literacy Rate Calculations

The literacy rate of a region is typically defined as the percentage of the population aged 7 and above who can both read and write with understanding. In the context of data interpretation problems like this one, "literate" usually refers to the count given in the table, and the "population" is the total count of individuals for whom literacy status is provided (literate + illiterate). The percentage of literates is calculated relative to this total population.

When combining data from multiple groups (like cities), the overall percentage is not the average of the individual percentages. Instead, you must calculate the total number of literate individuals and the total population for all groups combined, and then calculate the overall percentage using these totals. This is because the population sizes of the groups might be different, and a simple average would not account for the weighted contribution of each group.

For example, if City A had 75% literates out of 100 people and City B had 50% literates out of 1000 people, the overall percentage is not $(75\%+50\%)/2 = 62.5\%$. Instead, it's $(\frac{75+500}{100+1000}) \times 100 = (\frac{575}{1100}) \times 100 \approx 52.3\%$. This highlights the importance of using total population and total literate counts.