The question asks to find the principal amount based on the given simple interest (S.I.), rate, and time. The formula for simple interest is:

$S.I. = \frac{P \times R \times T}{100}$

Where:

• $P$ is the Principal amount,
• $R$ is the Rate of interest per annum,
• $T$ is the Time in years,
• $S.I.$ is the Simple Interest.

(a) Given:

• $S.I. = 720$
• $R = 2\%$
• $T = 3$ years

Using the formula:

$720 = \frac{P \times 2 \times 3}{100}$

Solving for $P$:

$720 = \frac{6P}{100}$

$P = \frac{720 \times 100}{6} = 12,000$

So, the principal amount is ₹12,000.

(b) Given:

• $S.I. = 4200$
• $R = 12\%$
• $T = 3 \frac{1}{2} = 3.5$ years

Using the formula:

$4200 = \frac{P \times 12 \times 3.5}{100}$

Solving for $P$:

$4200 = \frac{42P}{100}$

$P = \frac{4200 \times 100}{42} = 10,000$

So, the principal amount is ₹10,000.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How does changing the rate of interest affect the principal for a fixed simple interest?
2. How do you calculate compound interest, and how does it differ from simple interest?
3. What happens to the principal if the time is increased while keeping the rate and interest constant?
4. How would you solve for time if the principal and simple interest are known?
5. What is the effect of interest compounding annually, quarterly, or monthly?

Tip: Always make sure to convert mixed fractions (like $3\frac{1}{2}$) into decimal form before solving!