The ratio of ducks and frogs in a pond is `37 : 39` respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?

Options

A. 148
B. 152
C. 156
D. 144

Answer

To solve the problem, we need to find the number of frogs in the pond given the ratio of ducks to frogs and their average.

### Step-by-Step Solution:

1. **Understanding the Ratio**:
The ratio of ducks to frogs is given as 37:39. This means for every 37 ducks, there are 39 frogs.

2. **Letting x be the Multiplier**:
Let the number of ducks be \( 37x \) and the number of frogs be \( 39x \), where \( x \) is a common multiplier.

3. **Calculating the Total Number of Ducks and Frogs**:
The total number of ducks and frogs can be expressed as:
\[ \text{Total} = 37x + 39x = 76x \]

4. **Using the Average**:
We know the average number of ducks and frogs is 152. The average is calculated by dividing the total number of ducks and frogs by 2 (since there are two groups: ducks and frogs):
\[ \text{Average} = \frac{Total}{2} = \frac{76x}{2} = 38x \]
Setting this equal to the given average:
\[ 38x = 152 \]

5. **Solving for x**:
To find \( x \), divide both sides by 38:
\[ x = \frac{152}{38} = 4 \]

6. **Finding the Number of Frogs**:
Now that we have \( x \), we can find the number of frogs:
\[ \text{Number of frogs} = 39x = 39 \times 4 = 156 \]

### Final Answer:
The number of frogs in the pond is **156**.

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