Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A…

2024

Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?

  1. A.

    Rs. 6400

  2. B.

    Rs. 6409

  3. C.

    Rs. 6900

  4. D.

    Rs. 6700

Attempted by 2 students.

Show answer & explanation

Correct answer: A

Step-by-Step Solution

To find the amount invested in Scheme B, we can use the simple interest formula: S.I. = (P × R × T) / 100.

  1. Define the variables:

    • Let the amount invested in Scheme A be x.

    • Let the amount invested in Scheme B be (13900 - x).

    • Time (T) = 2 years.

    • Rate for Scheme A = 14% p.a.

    • Rate for Scheme B = 11% p.a.

    • Total Interest = Rs. 3508.

  2. Set up the equation:

    • Interest from Scheme A = (x × 14 × 2) / 100 = 28x / 100

    • Interest from Scheme B = ((13900 - x) × 11 × 2) / 100 = 22(13900 - x) / 100

    • Sum of interests: (28x / 100) + (22(13900 - x) / 100) = 3508

  3. Solve for x:

    • 28x + 22(13900 - x) = 350800

    • 28x + 305800 - 22x = 350800

    • 6x = 350800 - 305800

    • 6x = 45000

    • x = 7500 (Amount in Scheme A)

  4. Find the amount in Scheme B:

    • Amount in Scheme B = 13900 - 7500 = Rs. 6400.

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