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.

The correct option is 47:53.

To find the ratio between the investments in the two schemes, we can set up a system of linear equations based on the information provided in the question.

Step 1: Define variables for the two investments
Let the amount invested in the first scheme (offering 10% profit) be $x$ rupees.
Let the amount invested in the second scheme (offering 12% profit) be $y$ rupees.
Since the total amount invested is Rs. 100,000, we have our first equation:

$$x+y=\mathrm{100,000}$$

Step 2: Calculate the profit in both scenarios
In the first scenario, the profit obtained from the first scheme is 10% of $x$ and from the second scheme is 12% of $y$. Therefore, the total profit ($P_1$) is:

$$P_1=0.10x+0.12y$$

In the second scenario, the profit percentages are interchanged, meaning we get 12% profit on $x$ and 10% profit on $y$. The new total profit ($P_2$) is:

$$P_2=0.12x+0.10y$$

Step 3: Relate the two profit equations
We are given that the interchanged profit scenario results in Rs. 120 less profit. Thus, we can write:

$$P_1-P_2=120$$

Substituting the expressions for $P_1$ and $P_2$ into the equation:

$$(0.10x+0.12y)-(0.12x+0.10y)=120$$

Simplify this equation by grouping the terms containing $x$ and $y$:

$$-0.02x+0.02y=120$$

Divide the entire equation by 0.02 to solve for the difference between the investments:

$$y-x=\frac{120}{0.02}$$

$$y-x=\mathrm{6,000}$$

Step 4: Solve the system of linear equations
We now have two simple equations with two variables:
1) $y+x=\mathrm{100,000}$
2) $y-x=\mathrm{6,000}$

Adding the two equations together:

$$(y+x)+(y-x)=\mathrm{100,000}+\mathrm{6,000}$$

$$2y=\mathrm{106,000}$$

$$y=\mathrm{53,000}$$

Now, substitute the value of $y$ back into the first equation to find $x$:

$$x+\mathrm{53,000}=\mathrm{100,000}$$

$$x=\mathrm{100,000}-\mathrm{53,000}$$

$$x=\mathrm{47,000}$$

Step 5: Determine the ratio of the investments
The ratio of the investment in the first scheme to the second scheme is:

$$x:y=\mathrm{47,000}:\mathrm{53,000}$$

Dividing both sides by 1,000, we get the simplified ratio:

$$x:y=47:53$$