If the simple interest for 5 years is ₹77.50, find the simple interest for 4 years for the same principal and rate

Question

Accepted Answer

To determine the simple interest for 4 years given that the simple interest for 5 years is ₹77.50, we need to understand the relationship between time and simple interest. Simple interest is calculated using the formula:

$$ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} $$

where $ P $ is the principal amount, $ R $ is the rate of interest per annum, and $ T $ is the time in years.

Given that the simple interest for 5 years is ₹77.50, we can express this as:

$$ \frac{P \times R \times 5}{100} = 77.50 $$

To find the simple interest for 4 years, we use the same formula:

$$ \frac{P \times R \times 4}{100} = \text{Simple Interest for 4 years} $$

Since the principal $ P $ and rate $ R $ remain constant, the simple interest is directly proportional to the time period. Therefore, the simple interest for 4 years can be calculated by setting up a proportion based on the given 5-year interest:

$$ \frac{\text{SI for 4 years}}{\text{SI for 5 years}} = \frac{4}{5} $$

Substituting the known value:

$$ \frac{\text{SI for 4 years}}{77.50} = \frac{4}{5} $$

Solving for the simple interest for 4 years:

$$ \text{SI for 4 years} = 77.50 \times \frac{4}{5} $$

$$ \text{SI for 4 years} = 77.50 \times 0.8 $$

$$ \text{SI for 4 years} = 62 $$

Thus, the simple interest for 4 years is ₹62, which corresponds to Option 4.

**Explanation for Incorrect Options:**

1. **Option 1: ₹124** - This option is incorrect because it suggests a simple interest amount that is higher than the interest for 5 years, which is not possible since the time period is shorter.

2. **Option 2: ₹15.5** - This option is incorrect because it represents a much smaller amount than expected. The simple interest for 4 years should be a significant portion of the 5-year interest, not a fraction of it.

3. **Option 3: ₹387.5** - This option is incorrect because it is significantly higher than the interest for 5 years, which is illogical since the interest for a shorter period (4 years) should be less than that for 5 years.

Therefore, the correct answer is Option 4: ₹62, as it accurately reflects the simple interest for 4 years based on the given conditions.