A certain sum of money is invested for one year at a certain annual rate of simple interest. If the rate of interest is increased by 3 percentage points, then the interest earned in one year becomes 25 percent more than the interest earned earlier. What was the original annual rate of interest?

Introduction / Context:
This question deals with simple interest and the effect of changing the interest rate. The investment period is fixed at one year. We are told that increasing the rate by a fixed number of percentage points increases the interest amount by a certain percentage compared to the original interest. From this relationship, we must determine the original annual interest rate.

Given Data / Assumptions:

• Principal amount is some fixed sum P.
• Initial annual simple interest rate is r percent.
• Time period is one year in both cases.
• New annual rate is r + 3 percent.
• Interest at the new rate is 25 percent more than interest at the old rate.
• We must find r, the original rate of interest.

Concept / Approach:
For simple interest, the interest for one year equals principal multiplied by rate divided by 100, because time is one year. Let the original interest be I1 and the new interest be I2. Then I1 equals P * r / 100 and I2 equals P * (r + 3) / 100. We are told that I2 equals 1.25 times I1. Since P and 100 are common factors, they cancel out when we form the ratio, leaving an equation purely in terms of r. Solving this equation gives the original rate of interest.

Step-by-Step Solution:
Let principal be P rupees and original rate be r percent per annum.Original interest I1 equals P * r / 100.New rate is r + 3 percent per annum.New interest I2 equals P * (r + 3) / 100.According to the problem, the new interest is 25 percent more than the old interest, so I2 equals 1.25 * I1.Substitute the expressions: P * (r + 3) / 100 equals 1.25 * (P * r / 100).Cancel common factors P and 100 to obtain r + 3 equals 1.25 * r.Rewrite 1.25 * r as r + 0.25 * r.So the equation becomes r + 3 equals r + 0.25 * r, which simplifies to 3 equals 0.25 * r.Thus r equals 3 / 0.25 which is 12 percent per annum.

Verification / Alternative check:
We can verify by choosing a convenient principal, say P equals 100 rupees. At an original rate of 12 percent, the interest in one year is 12 rupees. If the rate increases by 3 percent, the new rate becomes 15 percent, giving an interest of 15 rupees. The increase in interest is 3 rupees, which is 25 percent of the original interest of 12 rupees, since 3 / 12 * 100 equals 25 percent. This numerical check confirms that 12 percent is indeed the correct original rate.

Why Other Options Are Wrong:
If the original rate were 4 percent, increasing the rate to 7 percent would make the interest 75 percent more, not 25 percent more. For 6 percent, increasing to 9 percent would produce a 50 percent increase in interest. For 8 percent, moving to 11 percent yields a 37.5 percent increase. Only 12 percent gives an increase from 12 to 15 rupees, which is exactly a 25 percent rise in the interest amount.

Common Pitfalls:
Some learners mistakenly interpret 3 percent higher as 3 percent of the original rate instead of three percentage points. Others forget that the principal and period remain constant, and they overcomplicate the calculation by including time factors unnecessarily. Writing down the simple interest formula for both cases and then forming the ratio is the easiest way to see that principal and time cancel out, leaving a simple linear equation in r.

Final Answer:
The original annual simple interest rate was 12 percent per annum.