The average of 5 consecutive odd numbers in descending order is 95. Find the fourth number in the descending order.

The correct option is 93.

Let us break down the solution step-by-step to understand why this is the correct answer.

We are given that there are 5 consecutive odd numbers arranged in descending order.

Let the 5 consecutive odd numbers in descending order be:
First number: $x$
Second number: $x-2$
Third number: $x-4$
Fourth number: $x-6$
Fifth number: $x-8$

The average of these 5 numbers is given as 95. The formula for the average is the sum of the numbers divided by the count of the numbers:

$\text{Average}=\frac{x+(x-2)+(x-4)+(x-6)+(x-8)}{5}=95$

Now, let us simplify the sum in the numerator:

$x+x-2+x-4+x-6+x-8=5x-20$

Substitute this back into our average equation:

$\frac{5x-20}{5}=95$

Divide each term in the numerator by 5:

$x-4=95$

Solving for $x$:

$x=95+4=99$

This means the first number (the largest number) in the descending order is 99. The five consecutive odd numbers in descending order are:
1st number: 99
2nd number: 97
3rd number: 95 (which is also the middle term and the average)
4th number: 93
5th number: 91

We need to find the fourth number in this descending order. Looking at the list, the fourth number is:

$x-6=99-6=93$

Thus, the fourth number in the descending order is 93.