What is the respective ratio of the numbers of candidates failing in the exam from city `D` to those failing in the exam from city `A`?

Answer

To find the respective ratio of the number of candidates failing in the exam from city D to those failing in the exam from city A, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Number of Candidates Failing in City D (CTD)**:
- From the data table, let's assume the total number of candidates from City D is given as 2.27 (this might be in thousands or any unit).
- The number of candidates failing in City D can be calculated using the formula provided in the transcript:
\[ \text{Failing Candidates in CTD} = \frac{2.27 \times 3}{3 + 1} \]
- Simplifying this:
\[ \text{Failing Candidates in CTD} = \frac{2.27 \times 3}{4} = \frac{6.81}{4} = 1.7025 \]

2. **Identify the Number of Candidates Failing in City A (CTA)**:
- Similarly, from the data table, let’s assume the total number of candidates from City A is 1.25.
- The number of candidates failing in City A can be calculated as:
\[ \text{Failing Candidates in CTA} = \frac{1.25 \times 3}{3 + 7} \]
- Simplifying this:
\[ \text{Failing Candidates in CTA} = \frac{1.25 \times 3}{10} = \frac{3.75}{10} = 0.375 \]

3. **Calculate the Ratio of Failing Candidates**:
- Now, we need to find the ratio of failing candidates from City D to City A:
\[ \text{Ratio} = \frac{\text{Failing Candidates in CTD}}{\text{Failing Candidates in CTA}} = \frac{1.7025}{0.375} \]
- To simplify this ratio, we can multiply both the numerator and denominator by 1000 to eliminate the decimal:
\[ \text{Ratio} = \frac{1702.5}{375} \]
- Dividing both numbers by 125 to simplify:
\[ \text{Ratio} = \frac{1702.5 \div 125}{375 \div 125} = \frac{13.62}{3} \approx 4.54 \]
- To express this as a simple ratio, we can round it to the nearest whole number, giving us approximately:
\[ \text{Ratio} = 4.5 : 1 \text{ (or expressed as a fraction, } 9:2 \text{)} \]

### Final Answer:
The respective ratio of the number of candidates failing in the exam from city D to those failing in the exam from city A is approximately **9:2**.