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    Amit invests a sum of Rs. 5400 and Gopal invests a sum of Rs. 9400 at the same rate of simple interest per annum. If, at the end of 5 years, Gopal get
    Question

    Amit invests a sum of Rs. 5400 and Gopal invests a sum of Rs. 9400 at the same rate of simple interest per annum. If, at the end of 5 years, Gopal gets Rs. 600 more interest than Amit, then find the rate of interest per annum (in percentage).

    A.

    3

    B.

    4

    C.

    2

    D.

    5

    Correct option is A

    Given:

    Amit invests ₹5400.

    Gopal invests ₹9400.

    The time period for both investments is 5 years.

    Gopal's interest is ₹600 more than Amit's interest.

    Formula Used:
    The formula for Simple Interest (SI) is:

    Simple Interest = P×R×T100 \frac{P \times R \times T}{100}​​

    where:

    P is the principal amount,

    R is the rate of interest per annum,

    T is the time in years.

    Solution:

    For Amit:

    SIA=5400×R×5100=27000R100=270R\text{SI}_A = \frac{5400 \times R \times 5}{100} = \frac{27000R}{100} = 270R​​

    For Gopal:

    SIG=9400×R×4100=47000R100=470R\text{SI}_G = \frac{9400 \times R \times 4}{100} = \frac{47000R}{100} = 470R​​

    The difference in interest between Gopal and Amit is ₹600:

    SIGSIA=600\text{SI}_G - \text{SI}_A = 600​​

    470R - 270R = 600

    200R = 600

    R=600200=3R = \frac{600}{200} = 3%

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