In a partnership business the monthly investment by three friends for the first six months is in the ratio $3: 4: 5$. After six months, they had to increase their monthly investments by $10 \%, 15 \%$ and $20 \%$, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months.
What is the ratio of their shares in the total profit $\text{(in the same order)}$ at the end of the year such that the share is proportional to their individual total investment over the year?
- $22: 23: 24
- $22: 33: 50
- $33: 46: 60
- $63: 86: 110$
