Akash borrowed Rs 12000 from a bank at the rate of 6\% for 8 years. After a certain period of time, the government introduced a scheme which reduced the interest rate by 3\%. At the end of 8 years, Akash paid Rs 16680 in total. After how many years was the scheme introduced?

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Accepted Answer

**Solution:**

1. Principal, $P = 12000$ Rs
2. Total time, $T = 8$ years
3. Initial interest rate, $R_1 = 6\%$
4. Reduced interest rate, $R_2 = 3\%$ (after scheme introduced)
5. Total amount paid after 8 years = Rs 16680

Calculate total interest paid:

$$
\text{Total Interest} = 16680 - 12000 = 4680 \text{ Rs}
$$

Let the scheme be introduced after $x$ years.

- Interest for first $x$ years at 6\%:
  $$
  I_1 = \frac{12000 \times 6 \times x}{100} = 720x
  $$

- Interest for remaining $8 - x$ years at 3\%:
  $$
  I_2 = \frac{12000 \times 3 \times (8 - x)}{100} = 360(8 - x) = 2880 - 360x
  $$

Total interest:

$$
I_1 + I_2 = 720x + 2880 - 360x = 360x + 2880
$$

Given total interest is 4680:

$$
360x + 2880 = 4680
$$

$$
360x = 4680 - 2880 = 1800
$$

$$
x = \frac{1800}{360} = 5 \text{ years}
$$

**Answer:** 5 years

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