A$,$ B$,$ and C formed a partnership with the following contributions: A $-$ Php $100,000$; B $-$ Php $50,000$; and C $-$ Php $50,000.$ The agreement on the sharing of profits is that, A will get $50\%$ of the profits and the other $50\%$ will go to C$.$ How much is the entitlement of B in such a case assuming a $1$M profit?

a$.$ Php $500,000$

b$.$ Php $250,000$

c$.$ Php $50,000$

d$.$ None of the above