Sixty percent of the rats included in particular experiment were female rats . If some of the rats died during the experiment and 30 percent of rats died were male , what was the ratio of the death rate among the male rats to the death rate among the famale rats ?

Options

A. `3:4`
B. `9:14`
C. `9:16`
D. `6:7`

Answer

To solve the problem step by step, let's break down the information provided and calculate the required ratio of the death rate among male rats to the death rate among female rats.

### Step 1: Determine the total number of rats
Let's assume the total number of rats in the experiment is 100. This assumption simplifies the calculations.

### Step 2: Calculate the number of female and male rats
Since 60% of the rats are female:
- Number of female rats = 60% of 100 = 60 female rats
- Number of male rats = 100 - 60 = 40 male rats

### Step 3: Define the total number of dead rats
Let’s assume that the total number of rats that died during the experiment is X.

### Step 4: Calculate the number of male and female rats that died
According to the problem, 30% of the dead rats were male:
- Number of male rats that died = 30% of X = 0.3X
- Therefore, the number of female rats that died = Total dead rats - Male dead rats = X - 0.3X = 0.7X

### Step 5: Calculate the death rate among male and female rats
To find the death rate among male and female rats, we need to compare the number of dead rats to the total number of each type of rat.

- Death rate among male rats = (Number of male rats that died) / (Total number of male rats)
\[ \text{Death rate among male rats} = \frac{0.3X}{40} \]

- Death rate among female rats = (Number of female rats that died) / (Total number of female rats)
\[ \text{Death rate among female rats} = \frac{0.7X}{60} \]

### Step 6: Set up the ratio of the death rates
Now, we need to find the ratio of the death rate among male rats to the death rate among female rats:
\[ \text{Ratio} = \frac{\text{Death rate among male rats}}{\text{Death rate among female rats}} = \frac{\frac{0.3X}{40}}{\frac{0.7X}{60}} \]

### Step 7: Simplify the ratio
To simplify the ratio, we can multiply by the reciprocal:
\[ \text{Ratio} = \frac{0.3X}{40} \times \frac{60}{0.7X} \]
The X cancels out:
\[ \text{Ratio} = \frac{0.3 \times 60}{40 \times 0.7} = \frac{18}{28} \]
Now simplify \( \frac{18}{28} \):
\[ \text{Ratio} = \frac{9}{14} \]

### Final Answer
The ratio of the death rate among male rats to the death rate among female rats is **9:14**.

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