Luqman and Pidris share profits and losses equally. Luqman and Pidris receive salary allowances of $$20,000$ and $$30,000,$ respectively, and both partners receive $10\%$ interest on their average capital balances. Pidris is entitled to a bonus of $10\%$ after deduction of bonus.$$ Partners$$ drawings are not used in determining the average capital balances. Total net income for $2024$ is $$275,000.$

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$$ Luqman$$ Pidris$$

January $1$ capital balances$$ $$100,000120,000$

Yearly drawings $($$$1,500$ a month$).18,00018,000$

Permanent withdrawals of capital:$$

$$ June $1(12,000)$

$$ May $1(15,000)$

Additional investments of capital:$$

$$ July $150,000$

$$ October $160,000$

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a$.$ What is the weighted$-$average capital for Luqman and Pidris in $2024?(12$ Points$)$

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$$b$.$ What will be the final profit allocations for Luqman and Pidris in $2024?(12$ points$).$