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Chhavi Balaji Jhaveri
Asked: 2022-11-11T12:56:39+05:30 In:

If the difference between the compound interest and simple interest at 17% on a sum of money for 2 years (compounded annually) is Rs. 433.50, then the sum (in Rs.) is:
1. 12,000
2. 20,000
3. 15,000
4. 25,000

If the difference between the compound interest and simple interest at 17% on a sum of money for 2 years (compounded annually) is Rs. 433.50, then the sum (in Rs.) is:
1. 12,000
2. 20,000
3. 15,000
4. 25,000
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1 Answer

  1. Correct Answer – Option 3 : 15,000

    Given:

    Rate of interest = 17%

    Time = 2 years

    The difference between CI and SI = Rs. 433.50

    Formula used:

    Simple interest = P × R% × T

    Calculation:

    Let the principal be Rs. x.

    SI = P × R% × T

    ⇒ SI = x × 17% × 2

    ⇒ SI = x × 17/100 × 2

    ⇒ SI = 34x/100

    ⇒ SI = 0.34x

    In the case of CI:

    1st year CI = P × R% × T

    ⇒ 1st year CI = x × 17% × 1

    ⇒ 1st year CI = 17x/100

    ⇒ 1st year CI = 0.17x

    Amount after 1st year = P + CI 

    ⇒ Amount = x + 0.17x

    ⇒ Amount = 1.17x

    2nd year CI = 1.17x × 17% × 1

    ⇒ 2nd year CI = 0.1989x

    Total CI = 1st year CI + 2nd year CI

    ⇒ CI = 0.17x + 0.1989x

    ⇒ CI = 0.3689x

    Required difference = CI – SI

    ⇒ 433.50 = 0.3689x – 0.34x

    ⇒ 433.50 = 0.0289x

    ⇒ x = 433.50/0.0289

    ⇒ x = Rs. 15000

    ∴ The sum is Rs. 15000.

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