Divide Rs. 8000 into two parts so that simple interest on first part for 3…

2024

Divide Rs. 8000 into two parts so that simple interest on first part for 3 years at 5% p.a. may be equal to simple interest on the second part for 5 years at 9% p.a.

  1. A.

    Rs. 2,000, Rs. 6,000

  2. B.

    Rs. 2,500, Rs. 5,500

  3. C.

    Rs. 3,000, Rs. 5,000

  4. D.

    None of these

Attempted by 4 students.

Show answer & explanation

Correct answer: A

Step-by-Step Solution

To divide Rs. 8000 into two parts such that the simple interest on both is equal, we can set up an equation based on the simple interest formula: S.I. = (P × R × T) / 100.

  1. Define the parts:

    • Let the first part be x.

    • Let the second part be (8000 - x).

  2. Set up the equation for equal interest:

    • Interest on first part = (x × 5 × 3) / 100

    • Interest on second part = ((8000 - x) × 9 × 5) / 100

    • Since the interests are equal: (15x) / 100 = (45 × (8000 - x)) / 100

  3. Solve for x:

    • 15x = 45(8000 - x)

    • Divide both sides by 15: x = 3(8000 - x)

    • x = 24000 - 3x

    • 4x = 24000

    • x = 6000

  4. Find the two parts:

    • First part (x) = Rs. 6000

    • Second part (8000 - x) = 8000 - 6000 = Rs. 2000

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