Question

Out of 7000, some amount was lent at 6% per annum and the remaining at 4% per annum. If the total simple interest from both the fractions in 5 years was 1600, find the sum lent at 6% per annum.

• A. 5000
• B. 34000
• C. 3000
• D. 2000

Answer 1

Answer:

D. 2000

Maths - Simple Interest

• Understanding the Problem: This problem involves calculating the principal amounts lent at two different interest rates, given the total principal, total interest earned over a period, and the individual interest rates.

• Key Concepts in Simple Interest: The formula for simple interest (SI) is: SI = (P * R * T) / 100, where P = Principal, R = Rate of Interest per annum, and T = Time in years.

• Setting up the Equations: Let 'x' be the amount lent at 6% per annum. Then, the remaining amount lent at 4% per annum will be (7000 - x).

• Calculating Interest for Each Part:

  • Interest from the amount lent at 6% for 5 years: SI₁ = (x * 6 * 5) / 100 = 30x / 100

  • Interest from the amount lent at 4% for 5 years: SI₂ = ((7000 - x) * 4 * 5) / 100 = (7000 - x) * 20 / 100

• Forming the Total Interest Equation: The total simple interest is given as 1600. So, SI₁ + SI₂ = 1600.

• Solving the Equation:

  • (30x / 100) + ((7000 - x) * 20 / 100) = 1600

  • Multiplying the entire equation by 100 to eliminate the denominators: 30x + 20(7000 - x) = 160000

  • Expanding the equation: 30x + 140000 - 20x = 160000

  • Simplifying: 10x + 140000 = 160000

  • Isolating the term with x: 10x = 160000 - 140000

  • 10x = 20000

  • Solving for x: x = 20000 / 10

  • x = 2000