7 men, 15 women can complete a piece of work in 15 days and the same work is completed by 18 men and 20 women in eight days. If X men and 20 women can complete the work in 10 days. Then find X.

To find the value of $X$, we can establish a relationship between the rates of work of men and women. Let the daily work done by one man be $m$ and by one woman be $w$.

From the first condition, 7 men and 15 women can complete the work in 15 days. Therefore, the total work ($W$) can be written as:
$W=15\times (7m+15w)$
$W=105m+225w$

From the second condition, 18 men and 20 women can complete the same work in 8 days. Therefore:
$W=8\times (18m+20w)$
$W=144m+160w$

Since the work done in both cases is the same, we equate the two expressions:
$105m+225w=144m+160w$

Rearranging the terms to solve for the relationship between $m$ and $w$:
$225w-160w=144m-105m$
$65w=39m$

Dividing both sides by 13 gives:
$5w=3m$
Hence, the ratio of work efficiency of a man to a woman is:
$m=\frac{5}{3}w$

Now, we can substitute $m=\frac{5}{3}w$ back into the first expression for total work $W$ in terms of $w$:
$W=105\left(\frac{5}{3}w\right)+225w$
$W=35\times 5w+225w$
$W=175w+225w$
$W=400w$

The third condition states that $X$ men and 20 women can complete the work in 10 days. Therefore:
$W=10\times (Xm+20w)$

Substitute $W=400w$ and $m=\frac{5}{3}w$ into this equation:
$400w=10\times \left(X\right(\frac{5}{3}w)+20w)$

Divide both sides by $10w$:
$40=\frac{5}{3}X+20$

Subtract 20 from both sides:
$20=\frac{5}{3}X$

Multiply both sides by $\frac{3}{5}$ to solve for $X$:
$X=20\times \frac{3}{5}$
$X=4\times 3$
$X=12$

Thus, the correct option is 12.