Consider ten consecutive odd numbers sarting from 5. Multiply each of them, except the first and the second, with three. What will be the average of the ten numbers so formed?

Options

A. 39.6
B. 39
C. 42
D. 38.4

Answer

To solve the problem step by step, we will follow these instructions:

1. **Identify the ten consecutive odd numbers starting from 5.**
- The sequence of ten consecutive odd numbers starting from 5 is:
5, 7, 9, 11, 13, 15, 17, 19, 21, 23.

2. **Select the numbers to be modified.**
- We will leave the first two numbers (5 and 7) unchanged and multiply the remaining eight numbers (9, 11, 13, 15, 17, 19, 21, 23) by 3.

3. **Multiply the selected numbers by 3.**
- The modified numbers will be:
- 9 × 3 = 27
- 11 × 3 = 33
- 13 × 3 = 39
- 15 × 3 = 45
- 17 × 3 = 51
- 19 × 3 = 57
- 21 × 3 = 63
- 23 × 3 = 69

4. **List all the numbers after modification.**
- The complete list of numbers now is:
5, 7, 27, 33, 39, 45, 51, 57, 63, 69.

5. **Calculate the sum of these numbers.**
- Sum = 5 + 7 + 27 + 33 + 39 + 45 + 51 + 57 + 63 + 69
- Sum = 5 + 7 = 12
- Sum = 12 + 27 = 39
- Sum = 39 + 33 = 72
- Sum = 72 + 39 = 111
- Sum = 111 + 45 = 156
- Sum = 156 + 51 = 207
- Sum = 207 + 57 = 264
- Sum = 264 + 63 = 327
- Sum = 327 + 69 = 396

6. **Calculate the average of the ten numbers.**
- Average = Total Sum / Number of Terms
- Average = 396 / 10 = 39.6

Thus, the average of the ten numbers formed is **39.6**.