Explanation:

- Let the initial investment be Rs. x.

- At 10% p.a. compound interest, after 2 years:

  Amount = x × (1.1)² = x × 1.21

- After 2 years, he invests half the initial amount again, i.e., x/2.

- Total interest after 3 years is Rs. 457.2.

Let’s break it:

For first investment (x):

- For first 2 years: Compound interest = x × (1.21 – 1) = 0.21x

- For third year, x continues for 1 year more:

  Amount after 2 years = x × 1.21

  Interest for 3rd year = x × 1.21 × 10% = 0.121x

For the second investment (x/2):

- Invested at the end of 2nd year for 1 year at 10% CI:

  Interest = (x/2) × 10% = 0.05x

Total interest:

0.21x + 0.121x + 0.05x = 0.381x = 457.2

So x = 457.2 / 0.381 = 1200

*Now, if Rs. 1200 is invested at 15% simple interest for 3 years:*

Interest = 1200 × 15% × 3 = 1200 × 0.45 = Rs. 540

Amount received = 1200 + 540 = Rs. 1740

The correct answer is:

Option:1, 1740 Rs.