Answer: Option D
Let the principal be P and the rate of interest be R% per annum.
According to the question:
Simple Interest = Rs. 256Rate of interest = Number of years
We know that the formula for simple interest is:
Simple Interest = (PRT)/100
Where P is the principal, R is the rate of interest and T is the time period in years.
From the given information, we can form the equation:
256 = (PRR)/10025600 = P*R^2
We need to find the rate of interest, which is R. To do this, we need to find the value of R from the equation.
We can factorize 25600 as follows:
25600 = 16160025600 = 1640*40
Substituting this in the equation, we get:
164040 = PR^2PR^2 = 164040
We can simplify this to:
PR^2 = (440)^2P*R^2 = 1600
Dividing both sides by P, we get:
R^2 = 1600/P
Taking the square root of both sides, we get:
R = √(1600/P)
Substituting the value of P in terms of R from the original equation, we get:
25600 = (R^2)*P25600 = R^2 * (1600/R^2)25600 = 1600
Therefore, R = 16
Hence, the rate of interest is 16% per annum, which is Option D.
Explanation:

• Simple Interest: Simple interest is the interest calculated on the principal amount only.
• Principal: The principal is the original amount of money invested or borrowed.
• Rate of Interest: The rate of interest is the percentage of the principal charged as interest by the lender or paid by the borrower.
• Time Period: The time period is the duration for which the money is borrowed or invested.
• We use the formula, Simple Interest = (PRT)/100 to calculate the simple interest on a given principal amount, rate of interest, and time period.
• In this question, we have formed an equation using the given information and then solved for the rate of interest.
• We found that the rate of interest is 16% per annum, which is Option D.

Note: It's important to understand the formula for simple interest and how to manipulate equations to arrive at the answer.