The sum of a series of 5 consecutive odd numbers is 195. The seconds lowest number of this series is 5 less than the second highest number of another series of 5 consecutive even numbers. What is `40%`of the second lowest number of the series of consecutive even numbers?

Options

A. 16.8
B. 18.8
C. 19.4
D. 15.2

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the first series of odd numbers
Let the first odd number be \( X \). The five consecutive odd numbers can be represented as:
- First odd number: \( X \)
- Second odd number: \( X + 2 \)
- Third odd number: \( X + 4 \)
- Fourth odd number: \( X + 6 \)
- Fifth odd number: \( X + 8 \)

### Step 2: Set up the equation for the sum of odd numbers
According to the problem, the sum of these five consecutive odd numbers is 195. Therefore, we can write the equation:
\[ X + (X + 2) + (X + 4) + (X + 6) + (X + 8) = 195 \]
This simplifies to:
\[ 5X + 20 = 195 \]

### Step 3: Solve for \( X \)
Now, we solve for \( X \):
\[ 5X = 195 - 20 \]
\[ 5X = 175 \]
\[ X = \frac{175}{5} = 35 \]

### Step 4: Identify the second lowest odd number
The first odd number is \( 35 \), so the second lowest odd number is:
\[ X + 2 = 35 + 2 = 37 \]

### Step 5: Define the second series of even numbers
Let the first even number be \( Y \). The five consecutive even numbers can be represented as:
- First even number: \( Y \)
- Second even number: \( Y + 2 \)
- Third even number: \( Y + 4 \)
- Fourth even number: \( Y + 6 \)
- Fifth even number: \( Y + 8 \)

### Step 6: Identify the second highest even number
The second highest even number in this series is:
\[ Y + 6 \]

### Step 7: Set up the relationship between the odd and even series
According to the problem, the second lowest odd number (which is \( 37 \)) is 5 less than the second highest even number. Therefore, we can write:
\[ 37 = (Y + 6) - 5 \]
This simplifies to:
\[ 37 = Y + 1 \]

### Step 8: Solve for \( Y \)
Now, we solve for \( Y \):
\[ Y = 37 - 1 = 36 \]

### Step 9: Identify the second lowest even number
The second lowest even number is:
\[ Y + 2 = 36 + 2 = 38 \]

### Step 10: Calculate 40% of the second lowest even number
To find 40% of \( 38 \):
\[ 40\% \text{ of } 38 = \frac{40}{100} \times 38 = 0.4 \times 38 = 15.2 \]

### Final Answer
Thus, the answer is \( 15.2 \).

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