The sum of the present ages of Amy and Beth is 50 years, and the sum of the present ages of Clara and Beth is 45 years. The ratio of Amy's age 10 years from now to Beth's age 5 years ago is 8 : X. If Clara's age 10 years from now is 35 years, then find the value of X.

The correct answer is 3.

Step 1: Determine the present age of Clara.

We are given that Clara's age 10 years from now will be 35 years.

Let Clara's present age be $C$.

$C+10=35$

$C=35-10=25\text{years}$

Step 2: Find the present age of Beth.

We are given that the sum of the present ages of Clara and Beth is 45 years.

Let Beth's present age be $B$.

$C+B=45$

$25+B=45$

$B=45-25=20\text{years}$

Step 3: Find the present age of Amy.

We are given that the sum of the present ages of Amy and Beth is 50 years.

Let Amy's present age be $A$.

$A+B=50$

$A+20=50$

$A=50-20=30\text{years}$

Step 4: Calculate Amy's age 10 years from now and Beth's age 5 years ago.

Amy's age 10 years from now:

$A+10=30+10=40\text{years}$

Beth's age 5 years ago:

$B-5=20-5=15\text{years}$

Step 5: Find the value of X using the given ratio.

The ratio of Amy's age 10 years from now to Beth's age 5 years ago is given as 8 : X.

$\frac{40}{15}=\frac{8}{X}$

Simplifying the fraction $\frac{40}{15}$ by dividing both the numerator and denominator by 5:

$\frac{8}{3}=\frac{8}{X}$

Comparing both sides, we get:

$X=3$

Thus, the value of X is 3.