Answer:
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).
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).