Maths-
General
Easy

Question

The simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time if both are numerically equal?

hintHint:

Use the formula of simple interest and then find rate of interest and number of years according to the information provided in the question.

The correct answer is: 8 years


    Complete step by step solution:
    Let the sum of money = P
    It is given that the simple interest SI is 16 over 25 of the sum, SI = 16 over 25 P
    Also given that rate percent and time, both are equal.
    That is, R = T
    We calculate simple interest by the formula,S I equals fraction numerator P T R over denominator 100 end fraction…(i)
    where P is Principal amount, T is number of years and R is rate of interest

    Here, we have S I equals 16 over 25 P comma R equals T equals ?
    On substituting the known values in (i), we get 16 over 25 P equals fraction numerator P cross times R cross times R over denominator 100 end fraction
    On dividing both the sides by P, we get 16 over 25 equals R squared over 100
    table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow R squared equals fraction numerator 16 cross times 100 over denominator 25 end fraction end cell row cell not stretchy rightwards double arrow R squared equals 64 end cell row cell not stretchy rightwards double arrow R equals square root of 64 equals 8 straight percent sign end cell end table
    Given that rate of interest = time , so R = T = 8
    Hence rate percent (R) = 8% and number of years = 8 years

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