Maths-
General
Easy

Question

At what percent of simple interest will the sum of money amount to 5/3 of itself in 6 years 8 months?

Hint:

It is given that A = 5 over 3 times the principal amount.

The correct answer is: 6 years and 8 months


    Complete step by step solution:
    Formula for total amount = A = P + SI…(i)
    where  is the total amount,  is the principal amount and  is simple interest .
    Here, A equals 5 over 3 P and 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 the rate of interest.
    It is given that time (T) = 6 years 8 months = open parentheses 6 plus 8 over 12 close parentheses equals open parentheses 20 over 3 close parentheses equals 6.666666667 years.
    We have, T = 6.66667 (given)
    On substituting these values in (i), we have 5 over 3 P equals P plus fraction numerator P cross times 6.66667 cross times R over denominator 100 end fraction.
    Subtract P from both sides.
    Then we have, 2 over 3 P equals fraction numerator P cross times 6.66667 cross times R over denominator 100 end fraction
    On further simplifications, we have 6.66667 R equals 200 over 3
    Then we get, R equals 200 over 20 equals 10 straight percent sign
    At 10% per annum the sum amount will be 5 over 3 itself in 6 years and 8 months.

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