Explanation:

Alright, let’s break down what’s going on here.

- Simple interest is one-fourth of the sum.

That means if the principal = P, then interest = P/4.

- Interest rate per year is four times the number of years.

Let the number of years = n, so the rate R = 4n % per annum.

- The formula:

S.I. = (P × R × n) / 100

We set up the equation

P/4 = (P × 4n × n)/100

- Solving for n:

P/4 = (P × 4n²)/100

Cross-multiplied:

100 = 16n²

n² = 100/16 = 6.25

n = 2.5 years (but we want S.I. for 3 years, so keep that in mind)

- Now, rate for 2.5 years is R = 4 × 2.5 = 10%.

If rate increases by 2%, new rate = 12%.

- Calculate S.I. for Rs5,000, 3 years, at 12%:

S.I. = (5000 × 12 × 3) / 100

= (5000 × 36) / 100

= 180,000 / 100

= Rs 1,800

Options:

1. 1,500

2. 2,000

3. 1,800

4. 300

So the right answer is Option 3, Rs 1,800.