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    A sum, when invested at 10% simple interest per annum, amounts to Rs. 4560 after 2 years. What is the simple interest (in Rs.) on the same sum at the
    Question

    A sum, when invested at 10% simple interest per annum, amounts to Rs. 4560 after 2 years. What is the simple interest (in Rs.) on the same sum at the same rate of interest in 1 year?

    A.

    1520

    B.

    380

    C.

    190

    D.

    760

    Correct option is B

    Given:

    Amount after 2 years = Rs. 4560

    Rate of interest = 10% p.a.

    Time = 2 years

    Formula Used:

    Amount = Principal + Simple Interest

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

    Solution:

    Let principal be P

    Then,

    4560 = P + P×10×2100\frac{P \times 10 \times 2}{100}​​

    4560 = P + 20P100 \frac{20P}{100}​​

    4560 = P(1+20100)P \left(1 + \frac{20}{100}\right)​​

    4560 = P×1.2P \times 1.2​​

    P =45601.2 \frac{4560}{1.2}​ = 3800

    Simple Interest for 1 year = 3800×10×1100=380 \frac{3800 \times 10 \times 1}{100} = 380​​

    Thus, The simple interest in 1 year is Rs. 380

    Alternate Solution: 

    10%=1SI10Principal10\% = \frac{1 \rightarrow \text{SI}}{10\rightarrow \text{Principal}}   

    SI for two year = 2 

    Amount = 10 + 2 = 12 

    12 unit = 4560 

    1 unit = 456012=380\frac{4560}{12} = 380 

    So, SI for 1 year = ₹ 380

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