Paltry and Sundry, the two bird hunters went to woods. Paltry fires 5 shots when Sundry fires 7 shots. But Paltry kills 2 out of 5 whike Sundry kills 3 out of 7. When Sundry has missed 32 shots, then how many birds has Paltry killed?

Options

A. 25
B. 24
C. 16
D. 12

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Shooting Ratios
Paltry fires 5 shots and kills 2 birds. Sundry fires 7 shots and kills 3 birds. We can determine the kill ratios for both hunters.

- **Paltry's kill ratio**:
\[ \text{Kill Ratio} = \frac{2}{5} \]

- **Sundry's kill ratio**:
\[ \text{Kill Ratio} = \frac{3}{7} \]

### Step 2: Calculate Miss Ratios
From the kill ratios, we can also determine the miss ratios.

- **Paltry's miss ratio**:
\[ \text{Miss Ratio} = 1 - \frac{2}{5} = \frac{3}{5} \]

- **Sundry's miss ratio**:
\[ \text{Miss Ratio} = 1 - \frac{3}{7} = \frac{4}{7} \]

### Step 3: Relate Missed Shots to Total Shots
We know that Sundry has missed 32 shots. We can use the miss ratio to find out how many shots Sundry has fired in total.

Let \( x \) be the total shots fired by Sundry. According to the miss ratio:
\[ \text{Missed Shots} = \frac{4}{7} \times x \]
Setting this equal to 32:
\[ \frac{4}{7} \times x = 32 \]

### Step 4: Solve for Total Shots Fired by Sundry
To find \( x \):
\[ x = 32 \times \frac{7}{4} = 56 \]
So, Sundry fired a total of 56 shots.

### Step 5: Calculate Total Shots Fired by Paltry
Now we can find out how many shots Paltry fired in the same ratio. Since Sundry fires 7 shots for every 5 shots fired by Paltry, we can set up the proportion:
\[ \frac{5}{7} = \frac{y}{56} \]
Where \( y \) is the total shots fired by Paltry. Solving for \( y \):
\[ y = 56 \times \frac{5}{7} = 40 \]
So, Paltry fired a total of 40 shots.

### Step 6: Calculate Birds Killed by Paltry
Using Paltry's kill ratio:
\[ \text{Birds Killed} = \frac{2}{5} \times 40 = 16 \]

### Final Answer
Paltry has killed **16 birds**.

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