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)?

The correct answer is Rs. 15000.

We are told the man invested a total of Rs. 44999.87 (approximately Rs. 45000) across two schemes:

- Scheme A: Simple Interest at 7.5% p.a.
- Scheme B: Simple Interest at 8% p.a.
- Time period: 2 years
- Ratio of Interest (A : B) = 15 : 8

Step 1: Set up variables.

Let the amount invested in Scheme A = Rs. x
Then, the amount invested in Scheme B = Rs. (45000 - x)

Step 2: Write the Simple Interest formulas for both schemes.

Simple Interest = \frac{P\times R\times T}{100}

Interest from Scheme A:

I_A=\frac{x\times 7.5\times 2}{100}=\frac{\mathrm{15x}}{100}

Interest from Scheme B:

I_B=\frac{(45000-x)\times 8\times 2}{100}=\frac{16(45000-x)}{100}

Step 3: Apply the given ratio condition.

\frac{I_A}{I_B}=\frac{15}{8}

Substituting:

\frac{15x}{16(45000-x)}=\frac{15}{8}

Step 4: Cross-multiply and solve for x.

8\times 15x=15\times 16(45000-x)

120x=240(45000-x)

120x=10800000-240x

120x+240x=10800000

360x=10800000

x=\frac{10800000}{360}=30000

Step 5: Find the amount invested in Scheme B.

Amount in Scheme B = 45000 - x = 45000 - 30000 = Rs. 15000

Verification:

- Interest from A = \frac{30000\times 7.5\times 2}{100}=4500

- Interest from B = \frac{15000\times 8\times 2}{100}=2400

- Ratio = 4500 : 2400 = 15 : 8 ✓

Therefore, the approximate amount invested in Scheme B is Rs. 15000.