A person invests Rs $X$ at 6\% simple interest for 5 years and earns Rs 1500 as interest. If he invests Rs $3X$ at 10\% compound interest for 2 years, what will be the amount he receives at the end of 2 years?

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**Solution:**

1. First, find the principal amount $X$ using the simple interest formula:
   $$	ext{Simple Interest} = \frac{P 	imes R 	imes T}{100}$$
   Given, Simple Interest = Rs 1500, Rate $R = 6\%$, Time $T = 5$ years.

Substitute values:
   $$1500 = \frac{X 	imes 6 	imes 5}{100}$$

2. Simplify to find $X$:
   $$1500 = \frac{30X}{100} = 0.3X$$
   $$X = \frac{1500}{0.3} = 5000$$

3. Now, the person invests Rs $3X = 3 	imes 5000 = 15000$ at 10\% compound interest for 2 years.

4. Calculate the amount using compound interest formula:
   $$A = P \left(1 + \frac{R}{100}ight)^T$$
   $$A = 15000 	imes \left(1 + \frac{10}{100}ight)^2 = 15000 	imes (1.1)^2 = 15000 	imes 1.21 = 18150$$

**Answer:** Rs 18150

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