Question

In △BCD, BP=15 cm.

Answer 1

we know that

The centroid is the point where all three medians intersect and divides each median in a ratio of $2:1$.  Is described as the triangle's center of gravity.

In this problem

C-Q, B-P and D-R ------> are medians

The point X is the centroid of the triangle BCD

so

$BX=\frac{2}{3}BP$

we have

$BP=15\ cm$

substitute

$BX=\frac{2}{3}(15)=10\ cm$

therefore

the answer is

$BX=10\ cm$

Answer 2

The answer is 10.

I PERSONALLY guessed it because it looks like BX is 10 and XP is 5 which is 15. (But I don't recommend always doing this because you might make a mistake when it comes to testing.)

HOWEVER: I confirmed it afterwards. The answer is still 10.