Task 570

The task

Find the ratio of the area of $\triangle BCX$ to the area of $\triangle ACX$ in the diagram if $CX$ bisects $\angle ACB$. Express your answer as a common fraction. [asy] import markers; real t=27/(27+30); pair A=(-15.57,0); pair B=(8.43,0); pair C=(0,25.65); pair X=t*A+(1-t)*B; draw(C--A--B--C--X); label("$A$",A,SW); label("$B$",B,E); label("$C$",C,N); label("$X$",X,NE); //markangle(n=1,radius=15,A,C,X,marker(markinterval(stickframe(n=1),true))); //markangle(n=1,radius=15,X,C,B,marker(markinterval(stickframe(n=1),true))); label("$24$",.5*(B+A),S); label("$27$",.5*(B+C),NE); label("$30$",.5*(A+C),NW); [/asy]