A$,$ B$,$ and C formed a partnership with the following contributions: A $-$ Php $100,000$; B $-$ Php $50,000$; and C $-$ Php $50,000.$ Assuming there is no agreement on the sharing of profits and the profits of the partnership amount to Php $1$ Million, how much is the entitlement of B$?$

a$.$ Php $250,000$

b$.$ Php $50,000$

c$.$ Php $500,000$

d$.$ Php $1,000,000$