Two numbers whose sum is 84 can not be in the ratio

Options

A. `5:7`
B. `13:8`
C. `1:3`
D. `3:2`

Answer

To solve the problem of determining which ratio cannot represent two numbers whose sum is 84, we will follow these steps:

### Step 1: Understand the Problem
We need to find out which of the given ratios cannot represent two numbers that add up to 84.

### Step 2: Identify the Ratios
Let's denote the ratios given in the options as follows:
1. Option A: 5:7
2. Option B: 13:8
3. Option C: 3:2
4. Option D: (Assuming another ratio for completion)

### Step 3: Calculate the Sum of the Ratios
For each ratio, we will calculate the sum of the parts of the ratio:
- For 5:7, the sum is \(5 + 7 = 12\).
- For 13:8, the sum is \(13 + 8 = 21\).
- For 3:2, the sum is \(3 + 2 = 5\).

### Step 4: Check Divisibility
Next, we will check if 84 is divisible by the sum of each ratio:
- For 5:7 (sum = 12):
\[ 84 \div 12 = 7 \quad (\text{divisible}) \]
- For 13:8 (sum = 21):
\[ 84 \div 21 = 4 \quad (\text{divisible}) \]
- For 3:2 (sum = 5):
\[ 84 \div 5 = 16.8 \quad (\text{not divisible}) \]

### Step 5: Conclusion
Since 84 is not divisible by the sum of the ratio 3:2, this ratio cannot represent two numbers whose sum is 84. Therefore, the answer is:
**Option C: 3:2.**