Question

What is the principal sum?
I. The interest amount after 30 months is half the interest amount after 5 years.
II. The sum amounts to Rs 750 in a five years at simple interest rate
III. The rate of interest is 8% p.a.

• A. I and III only
• B. II and III only
• C. I and II only
• D. I and III only, or II and III only

Answer 1

The Correct Option is B

To determine the principal sum, let's analyze the given statements.

Statement II: The sum amounts to Rs 750 in five years at a simple interest rate.

Statement III: The rate of interest is 8% per annum.

Using Statements II and III, we can find the principal sum by using the formula for simple interest: \(A = P(1 + \frac{rt}{100})\), where \(A\) is the amount, \(P\) is the principal, \(r\) is the rate of interest, and \(t\) is the time in years.

Here, \(A = 750\), \(r = 8\%\), and \(t = 5\) years.

Substitute these values into the formula:

\(750 = P(1 + \frac{8 \times 5}{100})\)

\(750 = P(1 + \frac{40}{100})\)

\(750 = P(1.4)\)

Solving for \(P\):

\(P = \frac{750}{1.4}\)

\(P = 535.71\)

Therefore, the principal sum is Rs 535.71.

Hence, using Statements II and III only, the principal sum can be determined.