The capitals of two partners in a business are $₹30,000$ and $₹45,000$ $.$The net profit after deducting expenses is $₹12,000$ $.$Find the profit of each partner in the ratio of capital invested by them$.$

Step $1:$To find the profit for each partner

Given capitals of two partners in a business are $₹30,000$ and $₹45,000$

Net profit $=$$₹12,000$

Step $2:$ Find the ratio of their capitals

Ratio of thier capitals $=30,000:45,000$

$=\frac{30000}{45000}$

$=\frac{30}{45}$

$=\frac{2}{3}$

$2:3$

Sum of the terms of the ratio $=2+3$

$=5$

Step $2:$ Now find the profit of each

Profit for the first capital $=\frac{2}{5}\times 12000$

$=2\times 2400$

$=4800$

Profit for the second capital $=\frac{3}{5}\times 12000$

$=3\times 2400$

$=7200$

Hence, the profit of the two partner in the business are $₹4800$ and $₹7200$