What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years? ( with explanation )

Ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years is 2:3 (2/3).

Step-by-step explanation:

SI for any amount p at r% annual rate in time t is given by

SI = p*r*t /100

p = principal amount

r = annual rate of interest

t = time period

As given  ratio of simple interest earned by certain amount at the same rate of interest

So, rate of interest  be r and  principal amount be p in both cases

simple interest earned  for 6 years = p*r*6/100

simple interest earned  for 9 years = p*r*9/100

let take ratio for both SI

simple interest earned  for 6 years/ simple interest earned  for 9 years

                                                 = (p*r*6/100 ) / (p*r*9/100 )

As p*r/ 100 in numerator and denominator is common , it gets cancelled

simple interest earned  for 6 years/ simple interest earned  for 9 years

                                                 =6/9 = 2/3

Thus, ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years is 2:3 (2/3).