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.
What is the ratio between graduate population of city C and total population of city B?

Options

A. `5:8`
B. `3:5`
C. `5:3`
D. `8:5`

Answer

To solve the problem step by step, we will analyze the information given about the populations of cities A, B, and C, and then calculate the required ratio.

### Step 1: Determine the total population of city C
We know that the total literate population of city B is 6000, which is 6.25% of the total population of city C. Let's denote the total population of city C as \( x \).

\[ 6000 = 6.25\% \text{ of } x \]

To convert 6.25% to a fraction:

\[ 6.25\% = \frac{6.25}{100} = \frac{1}{16} \]

Now, we can set up the equation:

\[ 6000 = \frac{1}{16} x \]

Multiplying both sides by 16 to solve for \( x \):

\[ x = 6000 \times 16 = 96000 \]

So, the total population of city C is **96,000**.

### Step 2: Calculate the literate and illiterate populations of city A
The ratio of literate to illiterate population in city A is given as 5:6. Let the literate population of city A be \( 5y \) and the illiterate population be \( 6y \).

The total population of city A is 22,000:

\[ 5y + 6y = 22000 \]

\[ 11y = 22000 \implies y = 2000 \]

Now substituting back to find the literate and illiterate populations:

- Literate population of city A: \( 5y = 5 \times 2000 = 10000 \)
- Illiterate population of city A: \( 6y = 6 \times 2000 = 12000 \)

### Step 3: Calculate the literate and illiterate populations of city C
The ratio of literate to illiterate population in city C is given as 2:1. Let the literate population of city C be \( 2z \) and the illiterate population be \( z \).

The total population of city C is 96,000:

\[ 2z + z = 96000 \]

\[ 3z = 96000 \implies z = 32000 \]

Now substituting back to find the literate and illiterate populations:

- Literate population of city C: \( 2z = 2 \times 32000 = 64000 \)
- Illiterate population of city C: \( z = 32000 \)

### Step 4: Calculate the graduate population in city C
40% of the literate population in city C is graduate:

\[ \text{Graduate population in city C} = 40\% \text{ of } 64000 = \frac{40}{100} \times 64000 = 25600 \]

### Step 5: Calculate the total population of city B
The total population of city B is given as 16,000.

### Step 6: Calculate the ratio of the graduate population of city C to the total population of city B
Now we need to find the ratio of the graduate population of city C (25,600) to the total population of city B (16,000):

\[ \text{Ratio} = \frac{\text{Graduate population of city C}}{\text{Total population of city B}} = \frac{25600}{16000} \]

To simplify this ratio:

\[ \frac{25600 \div 1600}{16000 \div 1600} = \frac{16}{10} = \frac{8}{5} \]

### Final Answer
The ratio between the graduate population of city C and the total population of city B is **8:5**.

---