Given:
The equivalent resistance of two resistors connected in series is 10 ohm.
The parallel equivalent resistance is 9/10 ohm.

To find:
The values of the resistances.

Solution:

We are given that the two resistors are connected in series and have an equivalent resistance of 10 ohm. Let's assume the resistances of the two resistors are R1 and R2.

Resistance in series:
When resistors are connected in series, the total resistance is the sum of individual resistances.
So, R_total = R1 + R2 = 10 ohm.

Resistance in parallel:
When resistors are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of individual resistances.
So, 1/R_total = 1/R1 + 1/R2.

Given that the parallel equivalent resistance is 9/10 ohm, we can write:
1/R_total = 1/R1 + 1/R2 = 9/10.

Solving the equations:
We have two equations:
1) R1 + R2 = 10
2) 1/R1 + 1/R2 = 9/10

Let's solve these equations to find the values of R1 and R2.

Method 1: Substitution
We can rearrange equation 1 to express R1 in terms of R2:
R1 = 10 - R2

Substituting this value into equation 2:
1/(10 - R2) + 1/R2 = 9/10

Solving this equation will give us the values of R1 and R2.

Method 2: Elimination
We can multiply equation 1 by R2:
R1 * R2 + R2 * R2 = 10 * R2

Substituting this value into equation 2:
R2 + (10 * R2) / (R2^2) = 9/10

Simplifying and solving this equation will give us the values of R1 and R2.

Comparing the options:
Using the solutions obtained from either method, we can compare the values of R1 and R2 with the given options (9ohm and 1ohm, 8ohm and 2ohm, 6ohm and 4ohm, 5ohm and 5ohm). The option that matches the values obtained from solving the equations will be the correct answer.

Conclusion:
By solving the equations obtained from the given information, we can determine the values of the resistances R1 and R2. Comparing these values with the given options, we can identify the correct answer.