A man invested 3000 in a bank at S I , if the rate of interest is increased by 4% then the interest is increased by 480 . Find the number of years:

Answer:

Principle (P): The initial amount invested or borrowed.
Rate of Interest (R): The percentage at which interest is calculated on the principal per annum.
Time (T): The duration for which the money is invested or borrowed, usually in years.
Simple Interest (SI): Interest calculated only on the principal amount. Formula: SI = (P * R * T) / 100
Amount (A): The total sum after adding interest to the principal. Formula: A = P + SI

Given:
- Principal (P) = ₹3000
- Increase in Rate of Interest = 4%
- Increase in Interest = ₹480
Analysis of the Interest Increase: The increase in interest (₹480) is directly due to the increase in the rate of interest (4%). This means that for a 4% increase in the rate, the interest earned over the same period (T) is ₹480.
Calculating Interest for the Rate Increase: We can use the SI formula to relate the increase in interest to the increase in rate. Let the original rate be R. The new rate is R + 4.
- Original Interest = (3000 × R × T) / 100
- New Interest = (3000 × (R + 4) × T) / 100
- Increase in Interest = New Interest - Original Interest
- 480 = [(3000 × (R + 4) × T) / 100] - [(3000 × R × T) / 100]
Simplifying the Equation:
- 480 = (3000 × T / 100) × [(R + 4) - R]
- 480 = (30 × T) × 4
- 480 = 120 × T
Solving for Time (T):
- T = 480 / 120
- T = 4 years

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