A man invested Rs.44999.87 in two different schemes A and B, which scheme A offers simple interest at rate of 7.5% p.a. and scheme B offers simple interest at rate of 8% p.a., If after two years, the ratio of interest received by man from scheme A to that of B is 15 : 8, then find the approximate amount invested by man in scheme B (in Rs)?

To find the approximate amount invested in scheme B, let us break down the problem step-by-step.

Let the amount invested in scheme A be $P_A$ and the amount invested in scheme B be $P_B$.
The total investment is:
$P_A+P_B=44999.87$ which is approximately $45000$ Rs.

The rate of simple interest for scheme A is $R_A=7.5\%$ per annum.
The rate of simple interest for scheme B is $R_B=8\%$ per annum.
The time period for both schemes is $T=2$ years.

The formula for Simple Interest (SI) is:
$SI=\frac{P\times R\times T}{100}$

Therefore, the interest received from scheme A is:
$I{I}_A=\frac{P_A\times 7.5\times 2}{100}$

The interest received from scheme B is:
$I{I}_B=\frac{P_B\times 8\times 2}{100}$

We are given the ratio of interest received from scheme A to scheme B is 15 : 8:
$\frac{I{I}_A}{I{I}_B}=\frac{15}{8}$

Substituting the expressions for $I{I}_A$ and $I{I}_B$:
$\frac{\frac{P_A\times 7.5\times 2}{100}}{\frac{P_B\times 8\times 2}{100}}=\frac{15}{8}$

Simplifying the equation by canceling the common terms $2$ and $100$:
$\frac{P_A\times 7.5}{P_B\times 8}=\frac{15}{8}$

Multiply both sides by 8:
$P_A\times 7.5=P_B\times 15$

Now, solve for the ratio of the principal amounts:
$\frac{P_A}{P_B}=\frac{15}{7.5}=2$

This means:
$P_A=2P_B$

Using the total sum of investments:
$P_A+P_B\approx 45000$
$2P_B+P_B=45000$
$3P_B=45000$
$P_B=15000$ Rs.

Thus, the approximate amount invested by the man in scheme B is Rs. 15000.