A sum of Rs. _________ is invested in scheme ‘A’ at an interest rate of 16% per annum for 5 years under simple interest. Then, 75% of the amount received from scheme ‘A’ is reinvested in scheme ‘B’, which offers compound interest at 20% per annum for 2 years. The total interest earned from scheme ‘B’ is Rs. _________.

Identify the correct pair of principal amount and interest from scheme ‘B’ from the following options:

Question

A sum of Rs. _________ is invested in scheme ‘A’ at an interest rate of 16% per annum for 5 years under simple interest. Then, 75% of the amount received from scheme ‘A’ is reinvested in scheme ‘B’, which offers compound interest at 20% per annum for 2 years. The total interest earned from scheme ‘B’ is Rs. _________.

Identify the correct pair of principal amount and interest from scheme ‘B’ from the following options:

Accepted Answer

**Solution:**

1. Let the principal invested in scheme A be Rs. *P*.

2. Scheme A offers simple interest at 16% per annum for 5 years.
   - Simple Interest (SI) = $ \frac{P \times 16 \times 5}{100} = 0.8P $
   - Total amount after 5 years = Principal + SI = $ P + 0.8P = 1.8P $

3. 75% of this amount is reinvested in scheme B:
   - Amount invested in scheme B = $ 0.75 \times 1.8P = 1.35P $

4. Scheme B offers compound interest at 20% per annum for 2 years.
   - Compound Interest (CI) formula: $ CI = A \times \left(1 + \frac{r}{100}\right)^n - A $
   - Here, $ A = 1.35P, r = 20\%, n = 2 $
   - Calculate CI:
     $$
     CI = 1.35P \times \left(1 + \frac{20}{100}\right)^2 - 1.35P = 1.35P \times (1.44) - 1.35P = 1.944P - 1.35P = 0.594P
     $$

5. We are given the interest from scheme B for each option, so set $ 0.594P = \text{given interest} $ and solve for $ P $.

- For option (a): Interest = Rs. 5049
  $$ 0.594P = 5049 \implies P = \frac{5049}{0.594} = 8500 $$
  Principal matches Rs. 8500, so option (a) is consistent.

- For option (b): Interest = Rs. 7722
  $$ 0.594P = 7722 \implies P = \frac{7722}{0.594} = 13000 $$
  Principal matches Rs. 13000, so option (b) is consistent.

- For option (c): Interest = Rs. 6336
  $$ 0.594P = 6336 \implies P = \frac{6336}{0.594} = 10666.67 $$
  Principal does not match Rs. 16000, so option (c) is inconsistent.

- For option (d): Interest = Rs. 5940
  $$ 0.594P = 5940 \implies P = \frac{5940}{0.594} = 10000 $$
  Principal does not match Rs. 7500, so option (d) is inconsistent.

**Conclusion:** Only options (a) and (b) have matching principal and interest values.

**Answer:** Only A & B

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