In each of the following questions a number serie is given. After the series a number is given followed by (a),(b),(c ),(d) and (e ). You have to complete the series starting with the number given, following the sequence of the original series and answer the questions that follow the series.
`{:(85,43,44,67.5,137,345),(125,(a),(b),(c),(d),(e)):}`
What will come in place of (c) ?

Options

A. 86
B. 107.5
C. 112.5
D. 97.5

Answer

To solve the number series problem, we need to identify the pattern in the given sequence of numbers: 85, 43, 44, 67.5, 137, 345. Then we will apply this pattern to find the missing values (a), (b), (c), (d), and (e) starting from the number 125.

### Step-by-Step Solution:

1. **Identify the Pattern in the Original Series:**
- The series is: 85, 43, 44, 67.5, 137, 345.
- Let's analyze the differences and ratios between consecutive terms.

- From 85 to 43:
\[ 85 - 43 = 42 \]
- From 43 to 44:
\[ 44 - 43 = 1 \]
- From 44 to 67.5:
\[ 67.5 - 44 = 23.5 \]
- From 67.5 to 137:
\[ 137 - 67.5 = 69.5 \]
- From 137 to 345:
\[ 345 - 137 = 208 \]

2. **Finding the Next Terms Using the Identified Pattern:**
- The differences we calculated are: 42, 1, 23.5, 69.5, 208.
- Now, let's see if there is a multiplication or division pattern:
- 85 to 43: \( \frac{85}{2} = 42.5 \) (approximately)
- 43 to 44: \( 43 + 1 = 44 \)
- 44 to 67.5: \( 44 \times 1.5 = 66 \) (approximately)
- 67.5 to 137: \( 67.5 \times 2 = 135 \) (approximately)
- 137 to 345: \( 137 \times 2.5 = 342.5 \) (approximately)

3. **Applying the Pattern to Find (a), (b), (c), (d), (e):**
- Starting from 125:
- (a): \( 125 \div 2 = 62.5 \)
- (b): \( 62.5 + 1 = 63.5 \)
- (c): \( 63.5 \times 1.5 = 95.25 \)
- (d): \( 95.25 \times 2 = 190.5 \)
- (e): \( 190.5 \times 2.5 = 476.25 \)

4. **Final Values:**
- (a) = 62.5
- (b) = 63.5
- (c) = 95.25
- (d) = 190.5
- (e) = 476.25

### Answer:
The value that will come in place of (c) is **95.25**.