Prakash invested Rs. 'x' at 25% p.a. simple interest for 3 years and Rs. (x + 400) at 20% p.a. compound interest, compounded annually for 2 years. The sum of the interest received from the two investments is Rs. 3746. Find the amount received when Rs. (x + 1000) is invested at 10% p.a. simple interest, for 4 years. Which of the following statements is true?
I. Rs. (x + 2600)
II. Rs. (1.5x + 1100)
III. Rs. {(4x/5) + 3200}

According to the question, (x × 25 × 3)/100 + (x + 400)[(1 + 20/100)² - 1] = 3746 Or, 0.75x + 0.44(x + 400) = 3746 Or, 0.75x + 0.44x + 176 = 3746 Or, 1.19x = 3570 Or, x = 3570/1.19 = Rs. 3000 Therefore, sum invested at 10% p.a. simple interest on (x + 1000) = Rs. 4000 Amount received = (4000 × 10 × 4)/100 + 4000 = Rs. 5600 For I: Amount received = Rs. (x + 2600) = 3000 + 2600 = Rs. 5600 Therefore, I is true. For II: Amount received = Rs. (1.5x + 1100) = 1.5 × 3000 + 1100 = Rs. 5600 Therefore, II is true. For III: Amount received = Rs. {(4x/5) + 3200} = (4 × 3000)/5 + 3200 = Rs. 5600 Therefore, III is true. Hence, the correct answer is D.