请教大牛一道输血狗。

pangpangshin

讨论稿25题，A产品卖了3 times as much as B, A 的profit是A 成本的80%，B 的profit 是B成本的20%，问profit占total 成本的多少。选项有45%，50%，60%。。。
不知道怎么做

citidandan

category  A            B
cost         ca           cb
price        pa           pb
profit       0.8ca       0.2cb

Also we know: pa = 3 pb; proft = price - cost.
Therefore,  for A's profit: 0.8ca = pa - ca; pa = 1.8ca
                for B's profit: 0.2cb = pb - cb; pb = 1.2cb
So ca/cb =(2/3) (pa/pb) = 2

The ratio of total profit/total cost = (0.8ca + 0.2cb) / (ca + cb) = (0.8 (ca/cb) + 0.2) / ((ca/cb) + 1)
                                                  = (1.6 + 0.2) /(2 + 1) = 60%

sumerlaws

A cost = 100 so A profit = 80 so A sales = 180
Cuz A sales = 3 B sales so B sales = 60
Then B proft =10 and B cost = 50...

So total cost = 150, total profit = 90, Ans = 3/5 = 60%

Sorry cant type Chinese now...