The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ?

Let the rate be R% p.a. Then,

$18001+\frac{R}{100}2-1800-\frac{1800*R*2}{100}=405$

$1800\frac{100+R}{2}-1-\frac{2R}{100}=405$

  $1800\frac{100+R2-10000-200R}{10000}=405$

$\iff$

$\frac{9}{5}*R2=405 \iff R2=\frac{405*5}{9}=225\iff R=15$ 
Rate = 15%.