Refusal for exchange

I purchased a few items for my daughter, the slip was not kept as the items bought fit her properly. After a top from the items was worn, it was washed only to then realise that it has factory fault. The sleeves are not the same size. They refused to exchange as I do not have the slip and it was a cash purchase. So are we then forced to buy on credit or card? Because we now need proof? Please assist. I called their customer care as well they say it's up to the managers approval.