Explanation:

Let's break down the statements and options:

- The amount after 2 years at a certain rate (let’s call it R%) becomes Rs. 15950.

- If the interest rate is increased by 60% (so new rate is 1.6R + R = 1.6R + R = 2.6R, wait: original + 60% = R + 0.6R = 1.6R), the amount becomes Rs. 16820 in the same time.

Calculations:

- Let Principal = P.

- Using simple interest formula: Amount = P + (P × R × T) / 100

- For first case: 15950 = P + (P × R × 2)/100

- For second case: 16820 = P + (P × 1.6R × 2)/100

Let's find P:

From first case: 15950 = P(1 + (2R/100))

From second case: 16820 = P(1 + (3.2R/100))

Subtract first from second:

16820 - 15950 = P((3.2R - 2R)/100)

870 = P(1.2R/100)

So, 87000 = P × 1.2R

Also from first case:

P = 15950 / (1 + (2R/100))

Now substitute P in the above:

87000 = (15950 / (1 + (2R/100))) × 1.2R

(1 + (2R/100)) × 87000 = 15950 × 1.2R

87000 + (87000 × 2R/100) = 15950 × 1.2R

87000 + 1740R = 19140R

87000 = 19140R - 1740R = 17400R

R = 87000 / 17400 = 5%

Now, options:

- Option 1: 5% This is correct!

- Option 2: 6.5%

- Option 3: 7%

- Option 4: 8%

- Option 5: None of these

Summary:

- We solved using simple interest formula.

- On calculation, R = 5%, matching Option 1.

- Therefore, the correct answer is Option 1: 5%