Qais & Zaki formed a partnership on February $10,2009.$ Qais contributed cash of $$150,000,$ while Zaki contributed inventory with a fair value of $$120,000.$ Due to Qais's expertise in selling, Zaki agreed that Qais should have $60$ percent of the total capital of the partnership. Qais and Zaki agreed to recognize goodwill. What is the total capital of the QZ partnership and the capital balance of Zaki after the goodwill is recognized?

a$.$ Total capital $$270,000$ and Zaki, Capital $$162,000$

b$.$ Total capital $$450,000$ and Zaki, Capital $$270,000$

c$.$ Total capital $$300,000$ and Zaki, Capital $$180,000$

d$.$ Total capital $$350,000$ and Zaki, Capital $$198,000$