There are 650 candidates from five different states to participate in a competition. From state 1, the number of candidates is `12%` of the total candidates. From state 2 there are one-fifth of the total candidates. There are `8%` of total candidates from state 3. The number of candidates from state 4 and state 5 is equal.
What is the ratio between the number of candidates from state 2 and state 3 ?

Options

A. `3 : 5`
B. `2 : 5`
C. `5 : 2`
D. `5 : 3`

Answer

To find the ratio between the number of candidates from state 2 and state 3, we will follow these steps:

### Step 1: Calculate the number of candidates from each state
1. **Total candidates** = 650
2. **Candidates from state 1** = 12% of 650
\[ \text{Candidates from state 1} = \frac{12}{100} \times 650 = 78 \]

3. **Candidates from state 2** = \( \frac{1}{5} \) of 650
\[ \text{Candidates from state 2} = \frac{1}{5} \times 650 = 130 \]

4. **Candidates from state 3** = 8% of 650
\[ \text{Candidates from state 3} = \frac{8}{100} \times 650 = 52 \]

5. **Candidates from state 4 and state 5**: Let the number of candidates from state 4 and state 5 be \( x \) each. Since the total number of candidates is 650, we can write:
\[ 78 + 130 + 52 + x + x = 650 \]
Simplifying this gives:
\[ 260 + 2x = 650 \]
\[ 2x = 650 - 260 = 390 \]
\[ x = \frac{390}{2} = 195 \]
Thus, candidates from state 4 = 195 and candidates from state 5 = 195.

### Step 2: Find the ratio between the number of candidates from state 2 and state 3
- Candidates from state 2 = 130
- Candidates from state 3 = 52

Now, we can find the ratio:
\[ \text{Ratio} = \frac{\text{Candidates from state 2}}{\text{Candidates from state 3}} = \frac{130}{52} \]

### Step 3: Simplify the ratio
To simplify \( \frac{130}{52} \):
1. Find the greatest common divisor (GCD) of 130 and 52.
- GCD of 130 and 52 is 26.
2. Divide both the numerator and the denominator by 26:
\[ \frac{130 \div 26}{52 \div 26} = \frac{5}{2} \]

### Final Answer
The ratio between the number of candidates from state 2 and state 3 is \( 5:2 \).

---