Question
A person invests Rs. 'a' at 35%
simple interest per annum for 4 years, and another Rs. (a + 300) at 40% compound interest per annum, compounded half-yearly for 1 year. The total interest from both investments is Rs. 6020. Determine the total amount obtained when Rs. (a + 800) is invested at 15% simple interest per annum for 3 years. Which of these statements is correct? I. Rs. (a + 2600) II. Rs. (1.25a + 1800) III. Rs. (3a/4 + 3400)Solution
ATQ, (a × 35 × 4) / 100 + (a + 300)(1 + 20)² – (a + 300) = 6020 Or, 7a / 5 + 0.44(a + 300) = 6020 Or, 9.2a = 29440 Or, a = 29440 / 9.2 = 3200 Therefore, sum invested at 15% p.a. simple interest on (a + 800) = 4000 Amount received = (4000 × 15 × 3) / 100 + 4000 = 5800 For I: Amount received = a + 2600 = 5800 → True For II: Amount received = 1.25a + 1800 = 5800 → True For III: Amount received = (3a / 4) + 3400 = 5800 → True
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