Maths-
General
Easy

Question

The simple interest on a certain sum for 3 ½ years at 12% per annum is Rs. 98 more than the simple interest on the same sum for 2 ½ years at 14% per annum. Find the sum.

Hint:

Equate both the cases and then find the sum.

The correct answer is: P=Rs 1400


    Complete step by step solution:
    Let the sum of money = P

    Case Ι
    Principal amount = P, Rate = 12% and time = 3.5 years
    We know the formula of Interest I = fraction numerator P T R over denominator 100 end fraction,
    where P is Principal amount, T is number of years and  is rate of interest
    On substituting the values, we get I equals fraction numerator p cross times 3.5 cross times 12 over denominator 100 end fraction equals fraction numerator 42 P over denominator 100 end fraction…(i)
    Case Ⅱ
    Principal amount = P, Rate = 14% and time = 2.5 years
    We know the formula of Interest I = fraction numerator P T R over denominator 100 end fraction,
    where P is Principal amount, T is number of years and  is rate of interest
    On substituting the values, we get I equals fraction numerator P cross times 2.5 cross times 14 over denominator 100 end fraction equals fraction numerator 35 P over denominator 100 end fraction…(ii)
    It is given that the simple interest for case I is Rs 98 more than the simple interest for case Ⅱ.
    So, fraction numerator 42 P over denominator 100 end fraction minus fraction numerator 35 P over denominator 100 end fraction equals 98
    fraction numerator 7 P over denominator 100 end fraction equals 98
    On multiplying  on both the sides, we get 7p = 9800
    Divide the above equation by 7 on both the sides,
    We get P = 1400
    Hence the sum P = Rs 1400

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