Scenario A: Partners A$,$ B$,$ and C operate a business with profit sharing ratios of $5$:$3$:$2,$ and capital balances of $$300,000,$ $$200,000,$ and $$100,000$ respectively. The total income for the year is $$300,000.$ Each partner receives a fixed salary of $$50,000,$ and they are entitled to earn $10\%$ interest on their capital balances. Calculate the total income allocated to Partner B$.$