If a sum of money at a certain rate of simple interest per year doubles in 5 years and at a different rate of simple interest per year becomes three times in 12 years, then the difference in the two rates of simple interest per year is

Case I,

Principal = interest

$herefore$ Rate $=frac{ ext { S.I. } imes 100}{ ext { Principal } imes ext { Time }}=frac{100}{5}=20 \%$ per annum

Case II,

$herefore$ Rate $=frac{ ext { S.I. } imes 100}{ ext { Principal } imes ext { Time }}$

$=frac{2 imes 100}{12}=frac{50}{3} \%$ per annum

∴ Required difference

$=left(20-frac{50}{3} ight) \%=left(frac{60-50}{3} ight) \%=frac{10}{3}=3 frac{1}{3} \%$