Paragraph given below gives information of literate and illiterate population out of total population of three cities i.e.A, B and C. Read the paragraph carefully and answer the following questions.
Total population of city A and B are 22000 and 16000 respectively. Total literate population of city B is 6000 which is 6.25% of total population of city C. Ratio of literate to illiterate population in city A and C is 5:6 and 2:1 respectively. 40% of literate population in each city is graduate.
If ratio of male to female in graduate population from each city is 9:7, find difference between graduate male from city C to literate but ungraduated from city B?

Options

A. 7200
B. 14400
C. 10800
D. 12000

Answer

To solve the problem step by step, we will break down the information provided and calculate the required values.

### Step 1: Determine the total population of city C
From the problem, we know that the total literate population of city B is 6000, which is 6.25% of the total population of city C.

Let the total population of city C be \( x \).
According to the problem:
\[ 6000 = 6.25\% \text{ of } x \]
Converting 6.25% to a decimal:
\[ 6.25\% = \frac{6.25}{100} = 0.0625 \]
So, we have:
\[ 6000 = 0.0625x \]
To find \( x \):
\[ x = \frac{6000}{0.0625} = 96000 \]
Thus, the total population of city C is **96,000**.

### Step 2: Calculate the literate and illiterate populations in cities A and C
- **City A**: The ratio of literate to illiterate population is 5:6.
Let the literate population be \( 5k \) and the illiterate population be \( 6k \).
Total population of city A = 22,000.
\[ 5k + 6k = 22000 \implies 11k = 22000 \implies k = 2000 \]
Thus, the literate population in city A is:
\[ 5k = 5 \times 2000 = 10000 \]
And the illiterate population is:
\[ 6k = 6 \times 2000 = 12000 \]

- **City C**: The ratio of literate to illiterate population is 2:1.
Let the literate population be \( 2m \) and the illiterate population be \( m \).
Total population of city C = 96,000.
\[ 2m + m = 96000 \implies 3m = 96000 \implies m = 32000 \]
Thus, the literate population in city C is:
\[ 2m = 2 \times 32000 = 64000 \]
And the illiterate population is:
\[ m = 32000 \]

### Step 3: Calculate the graduate population in each city
40% of the literate population in each city is graduate.

- **City A**:
\[ \text{Graduate population} = 40\% \text{ of } 10000 = 0.4 \times 10000 = 4000 \]

- **City B**:
\[ \text{Graduate population} = 40\% \text{ of } 6000 = 0.4 \times 6000 = 2400 \]

- **City C**:
\[ \text{Graduate population} = 40\% \text{ of } 64000 = 0.4 \times 64000 = 25600 \]

### Step 4: Calculate the number of graduate males in city C
The ratio of male to female in the graduate population is 9:7.

Total graduate population in city C = 25600.
Total parts = 9 + 7 = 16.

Thus, the number of graduate males in city C:
\[ \text{Graduate males in C} = \frac{9}{16} \times 25600 = 14400 \]

### Step 5: Calculate the number of literate but ungraduated individuals in city B
Total literate population in city B = 6000.
Graduate population in city B = 2400.

Literate but ungraduated individuals in city B:
\[ \text{Literate but ungraduated} = 6000 - 2400 = 3600 \]

### Step 6: Calculate the difference between graduate males from city C and literate but ungraduated from city B
\[ \text{Difference} = \text{Graduate males in C} - \text{Literate but ungraduated in B} \]
\[ \text{Difference} = 14400 - 3600 = 10800 \]

### Final Answer
The difference between graduate males from city C and literate but ungraduated from city B is **10,800**.

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