You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows.
`{:("16","24","36","54","81","121.5"),("14","A","B","C","D","E"):}`
What will come in place of B?

Options

A. 34
B. `31(1)/(2)`
C. `30(1)/(2)`
D. 32

Explanation

To solve the problem, we will analyze the first series to identify the pattern and then apply that pattern to the second series to find the value of B.

### Step-by-Step Solution:

1. **Identify the Pattern in the First Series:**
The first series is: 16, 24, 36, 54, 81, 121.5.
We need to determine how each number relates to the previous one.

- From 16 to 24:
\[ 24 = 16 \times \frac{3}{2} \]
- From 24 to 36:
\[ 36 = 24 \times \frac{3}{2} \]
- From 36 to 54:
\[ 54 = 36 \times \frac{3}{2} \]
- From 54 to 81:
\[ 81 = 54 \times \frac{3}{2} \]
- From 81 to 121.5:
\[ 121.5 = 81 \times \frac{3}{2} \]

The pattern is that each number is obtained by multiplying the previous number by \(\frac{3}{2}\).

2. **Apply the Pattern to the Second Series:**
The second series starts with 14 and has elements A, B, C, D, E.
We will find A first.

- **Finding A:**
\[ A = 14 \times \frac{3}{2} = 21 \]

- **Finding B:**
\[ B = A \times \frac{3}{2} = 21 \times \frac{3}{2} = \frac{63}{2} = 31.5 \]

3. **Conclusion:**
The value that will come in place of B is \(31.5\).