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    If at same rate of interest, in 2 years, the simple interest is Rs. 42 and compound interest is Rs. 45, then what is the principal (in Rs. )?
    Question

    If at same rate of interest, in 2 years, the simple interest is Rs. 42 and compound interest is Rs. 45, then what is the principal (in Rs. )?

    A.

    147

    B.

    151

    C.

    140

    D.

    142

    Correct option is A

    Given:

    Simple Interest (SI) for 2 years = Rs. 42

    Compound Interest (CI) for 2 years = Rs. 45

    Same rate of interest, same principal

    Concept Used:

    Simple Interest (SI) is uniform each year.

    Compound Interest (CI) adds interest on interest.

    Difference between CI and SI in 2 years gives extra interest = interest on 1st year’s interest.

    Formula Used:

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

    CI - SI = P×R21002\frac{P \times R^2}{100^2}​​

    Solution:

    SI for 2 years = 42 

    SI for 1 year = 21

    CI for 2 years = 45 

    CI for 1st year = 21, CI for 2nd year = 24

    Extra interest = 24 - 21 = 3 = interest on Rs. 21

    R = 321×100=1007%14.28%\frac{3}{21} \times 100 = \frac{100}{7} \% \approx 14.28\%​​

    From SI formula (1 year):

    21 = P×1007100\frac{P \times \tfrac{100}{7}}{100}​​

    21 = P7\frac{P}{7}​​

    P = 147 

    Alternate Solution(Exam-hall Method): 

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