Question

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:

• A. 5
• B. 4
• C. 3
• D. 6

Answer 1

Answer:

B. 4

Simple Interest (SI) Concepts for Competitive Exams

• 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

Problem Breakdown and Solution

• 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