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A person divided an amount of Rs. $100,000$ into two parts and invested in two different schemes. In one he got $10 \%$ profit and in the other he got $12 \%$. If the profit percentages are interchanged with these investments he would have got Rs. $120$ less. Find the ratio between his investments in the two schemes.

- $9:16$
- $11:14$
- $37:63$
- $47:53$