Firstly, for the two categories, highest scores can be 131 and 170 respectively.
If we take a possible case wherein for the first category of 10 students we have 110,131,131,…131 and for the second we have 129,129,…129,170.
Here, the combined values will be arranged as 110, 129, 129,…(10 times 129), 131,…170.
The median will be the 11th value which in this case is 129.
If for another case for the first category of 10 students we have 110,128,128,…(128 8 times), 131 and for the second we have 129,170,…170,170.
Here, the combined values will be arranged as 110, 128, 128,…(8 times 128), 129, 131,…170.
The median will be the 11th value which in this case is 131.
Hence I think it should be option D.