Pulleys

Can someone explain part C for me please. The markscheme says the answer is 3kg as I’ve worked out on the right but my workings get m=2kg since I thought we’d resolve upwards since the particle will accelerate upwards surely? So why have they resolved the other way? Thanks
https://imgur.com/a/HvnWIVm

Your answer looks ok to me. Possible typo in the model solution, where does it come from?
If it was 3kg, the tension in the string to hold it in equilibrium would be ~30N, and you'd need extra tension to accelerate upwards. 2kg seems right.

Here’s the markscheme
https://imgur.com/a/b7cMqVp

I think they've got it wrong. If the tension is 23N and the mass is 3kg, the mass will move downwards.