A man invested Rs. $(X - 2500)$ on simple interest for 5 years and 3 days at an interest rate of 8.006\% per annum in scheme A. He also invested Rs. $X$ on compound interest for 2 years and 2 days at a rate of 10\% per annum in scheme B. If the approximate difference between the interest received from both schemes is Rs. 900, find the amount invested in scheme A (in Rs.).

Question

Accepted Answer

**Solution:**

1. Since the question involves approximate values, we will use rounded figures for easier calculation.

2. Calculate the simple interest from scheme A:
   - Principal = $(X - 2500)$
   - Rate = $8\%$ (approximate from 8.006\%)
   - Time = 5 years (ignoring 3 days as negligible for approximation)

Simple Interest (SI) = $\frac{P 	imes R 	imes T}{100} = \frac{(X - 2500) 	imes 8 	imes 5}{100} = 0.4X - 1000$

3. Calculate the compound interest equivalent rate for scheme B:
   - Principal = $X$
   - Rate = $10\%$ per annum
   - Time = 2 years (ignoring 2 days for approximation)

Compound Interest (CI) for 2 years at 10\% p.a.:
   $$CI = P 	imes \left(1 + \frac{R}{100}ight)^T - P = X 	imes (1.1)^2 - X = X 	imes (1.21 - 1) = 0.21X$$

4. According to the problem, the difference between the interest amounts is Rs. 900:
   $$SI - CI = 900$$
   Substituting values:
   $$0.4X - 1000 - 0.21X = 900$$
   $$0.19X - 1000 = 900$$
   $$0.19X = 1900$$
   $$X = \frac{1900}{0.19} = 10000$$

5. The amount invested in scheme A is:
   $$X - 2500 = 10000 - 2500 = 7500$$

**Answer:** Rs. 7500

Answer

Answer

Answer

Answer