It takes X weeks for Party A to do it alone and Y weeks for Party B to do it alone, so Party A does 1/x and Party B does 1/y every week, which takes 6 weeks altogether, that is to say,

6( 1/x+ 1/y)= 1

And a can be completed in four weeks and nine weeks, so 4/x+9/y= 1,

solve

x= 10，

y= 15

Then calculate the price.

Party A charges 1 10,000 yuan per week and Party B charges 1 10,000 yuan per week, so there are

6a+6b=5.2，

4a+9b=4.8，

solve

a=0.6，

b=4/ 15

So A needs to pay 0.6 *10 = 60,000 yuan.

B Need15 * 4/15 = 40,000 yuan.

So you should choose B.