If in the given number “ 357986258” the digits at the odd position are increased by 1 then the digits are arranged in descending order from left to right then what is the product of the 4th digits from both the ends in the new number thus formed?

The correct option is 40.

Let's break down the solution step-by-step:

Step 1: Identify the positions of the digits in the given number
The given number is 357986258. Let's write down the digits with their positions from left to right:
1st position (odd): 3
2nd position (even): 5
3rd position (odd): 7
4th position (even): 9
5th position (odd): 8
6th position (even): 6
7th position (odd): 2
8th position (even): 5
9th position (odd): 8

Step 2: Increase the digits at the odd positions by 1
According to the rule, the digits at the odd positions (1st, 3rd, 5th, 7th, and 9th positions) are increased by 1, while the digits at the even positions (2nd, 4th, 6th, and 8th positions) remain unchanged:
1st position: 3 + 1 = 4
2nd position: 5 (remains unchanged)
3rd position: 7 + 1 = 8
4th position: 9 (remains unchanged)
5th position: 8 + 1 = 9
6th position: 6 (remains unchanged)
7th position: 2 + 1 = 3
8th position: 5 (remains unchanged)
9th position: 8 + 1 = 9

The new sequence of digits is: 4, 5, 8, 9, 9, 6, 3, 5, 9.

Step 3: Arrange the digits in descending order from left to right
Sorting the modified digits in descending order gives:
9, 9, 9, 8, 6, 5, 5, 4, 3

Step 4: Find the 4th digits from both ends
- Counting from the left end (left-to-right): The 4th digit is 8.
- Counting from the right end (right-to-left): The 4th digit is 5.

Step 5: Calculate the product of these two digits
The product of the 4th digit from the left end and the 4th digit from the right end is:

$8\times 5=40$