Analyzing City Population Data

The problem provides a table showing the percentage distribution of the total population across six cities (A to F) and the percentage of the adult population within each city. We are given the actual population of City A and asked to find the approximate percentage by which the population of City D is more than the population of City E.

We are given that the population of City A is 257400. The table shows that City A represents 23.4% of the total population of all six cities. We can use this information to find the total population.

Calculating Total Population

Let the total population of all six cities be $P_{\text{total}}$.

Population of City A = 23.4% of $P_{\text{total}}$

We can write this as:

$\text{Population of City A} = \left(\frac{23.4}{100}\right) \times P_{\text{total}}$

Given, Population of City A = 257400. So,

$257400 = \left(\frac{23.4}{100}\right) \times P_{\text{total}}$

Solving for $P_{\text{total}}$:

$P_{\text{total}} = \frac{257400 \times 100}{23.4}$

$P_{\text{total}} = \frac{25740000}{23.4}$

$P_{\text{total}} \approx 1100000$

So, the total population of all six cities is approximately 1100000.

Finding Population of City D and City E

Now we can find the population of City D and City E using their respective percentage distributions from the total population.

Population of City D = 18.9% of $P_{\text{total}}$

Population of City D $= \left(\frac{18.9}{100}\right) \times 1100000$

Population of City D $= 0.189 \times 1100000$

Population of City D $= 207900$

Population of City E = 17.5% of $P_{\text{total}}$

Population of City E $= \left(\frac{17.5}{100}\right) \times 1100000$

Population of City E $= 0.175 \times 1100000$

Population of City E $= 192500$

Calculating the Percentage Difference

We need to find by what percentage the population of City D is more than the population of City E. First, let's find the difference in their populations.

Difference = Population of City D - Population of City E

Difference $= 207900 - 192500$

Difference $= 15400$

Now, we express this difference as a percentage of the population of City E, because the question asks "more than the population of City E".

Percentage Difference $= \left(\frac{\text{Difference}}{\text{Population of City E}}\right) \times 100\%$

Percentage Difference $= \left(\frac{15400}{192500}\right) \times 100\%$

Percentage Difference $\approx 0.08 \times 100\%$

Percentage Difference $\approx 8\%$

Thus, the population of City D is approximately 8% more than the population of City E.

Comparing with Options

The calculated percentage difference is approximately 8%, which matches Option 1.

Revision Table: Population Distribution Analysis

• Given Data: Population of City A and percentage distribution for cities A-F.
• Goal: Find approximate percentage difference between population of City D and City E, relative to City E.
• Step 1: Calculate total population using City A's data.
• Step 2: Calculate population of City D.
• Step 3: Calculate population of City E.
• Step 4: Calculate the difference (City D - City E).
• Step 5: Calculate percentage difference relative to City E.

Additional Information: Understanding Percentage Differences

When comparing two values, say A and B, the percentage difference can be calculated in a couple of ways depending on the base value:

• Percentage A is more than B: $\left(\frac{A - B}{B}\right) \times 100\%$
• Percentage B is less than A: $\left(\frac{A - B}{A}\right) \times 100\%$

In this problem, the phrasing "population of City D is approximately ________ more than the population of City E" means we should use the population of City E as the base for comparison.

Data interpretation problems often require calculating total values from partial information (like finding total population from a known part) and then using these totals to find values for other parts or to make comparisons.