Maths-
General
Easy

Question

The amounts of certain sum of money with simple interest at certain rate of interest are Rs. 5440 in 3 years and Rs. 6440 in 5 years. Find the sum and rate of interest?

Hint:

Frame 2 equations from the information provided and find the ratios.

The correct answer is: 3951 Rupees


    Complete step by step solution:
    Let the sum of money = P and rate of interest = R
    Case Ⅰ
    We calculate simple interest by the formula, S I equals fraction numerator P T R over denominator 100 end fraction
    where P is Principal amount, T is number of years and R is rate of interest
    We are given T = 3.
    So, Simple interest for 3 years = S I equals fraction numerator P cross times 3 cross times R over denominator 100 end fraction
    Formula for total amount = A = P + SI,
    where A is the total amount, P is the principal amount and SI is simple interest .
    We have A = 5440 and S I equals fraction numerator p cross times 3 cross times R over denominator 100 end fraction.
    On substitution, we get A equals 5440 equals p plus fraction numerator p cross times 3 cross times R over denominator 100 end fraction…(i)
    Case Ⅱ
    We calculate simple interest by the formula, S I equals fraction numerator P T R over denominator 100 end fraction
    Here we have T = 5.
    So, Simple interest for 5 years = S I equals fraction numerator P cross times 5 cross times R over denominator 100 end fraction
    Formula for total amount = A = P + SI,
    We have A = 6440 and S I equals fraction numerator P cross times 5 cross times R over denominator 100 end fraction.
    On substitution, we get A equals 6440 equals p plus fraction numerator p cross times 5 cross times R over denominator 100 end fraction…(ii)
    Form (i) and (ii), we have
    fraction numerator 6440 over denominator open parentheses 1 plus fraction numerator 5 R over denominator 100 end fraction close parentheses end fraction equals fraction numerator 5440 over denominator open parentheses 1 plus fraction numerator 3 R over denominator 100 end fraction close parentheses end fraction
    This can be written as fraction numerator 6440 over denominator left parenthesis 100 plus 5 R right parenthesis end fraction equals fraction numerator 5440 over denominator left parenthesis 100 plus 3 R right parenthesis end fraction
    On cross multiplication, we get 6440 + 1932R = 54400 + 2720R
    On rearranging the above equation, we get 788R + 10000
    Divide on both the sides by 788.
    On dividing, we get R equals 12.6 straight percent sign
    Substitute R equals 12.6 straight percent sign in (ii).
    Then we get 6440 equals p plus fraction numerator p cross times 5 cross times 12.6 over denominator 100 end fraction
    not stretchy rightwards double arrow 6440 equals 1.63 P
    On simplifications, we get P = 3950.9 which can be rounded to Rs 3951.
    So principal amount = 3951 Rupees.

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