Maths-
General
Easy

Question

A sum of money lent out at simple interest amounts to Rs. 1240 in 4 years and Rs 1360 in 6 years. Find the sum and rate percent?

Hint:

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

The correct answer is: 1000 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 = 4.
    So, Simple interest for 4 years = S I equals fraction numerator P cross times 4 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 = 1240 and S I equals fraction numerator P cross times 4 cross times R over denominator 100 end fraction.
    On substitution, we get A equals 1240 equals p plus fraction numerator p cross times 4 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 = 6.
    So, Simple interest for 6 years = SI = fraction numerator P cross times 6 cross times R over denominator 100 end fraction
    Formula for total amount = A = P + SI,
    We have A = 1360 and SI = fraction numerator P cross times 6 cross times R over denominator 100 end fraction.
    On substitution, we get A = 1360 = p + fraction numerator P cross times 6 cross times R over denominator 100 end fraction…(ii)
    Form (i) and (ii), we have
    fraction numerator 1360 over denominator open parentheses 1 plus fraction numerator 6 R over denominator 100 end fraction close parentheses end fraction equals fraction numerator 1240 over denominator open parentheses 1 plus fraction numerator 4 R over denominator 100 end fraction close parentheses end fraction
    This can be written as fraction numerator 1360 over denominator left parenthesis 100 plus 6 R right parenthesis end fraction equals fraction numerator 1240 over denominator left parenthesis 100 plus 4 R right parenthesis end fraction
    On cross multiplication, we get 13600 + 544R = 12400 + 744R
    On rearranging the above equation, we get 200R = 1200
    Divide on both sides by 200.
    On dividing, we get R = 6%
    Substitute R = 6% in (ii).
    Then we get 1360 = p + fraction numerator P space cross times 6 cross times 6 over denominator 100 end fraction
    not stretchy rightwards double arrow 136000 equals 136 P
    On simplifications, we get P = 1000.
    So principal amount P = 1000 Rupees.

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