On dividing a number by 9, the remainder is 8. The quotient so obtained when divided by 11 leaves remainder 9. The next quotient when divided by 13 leaves remainder 8. What is the remainder when the original number is divided by 1287?

Let the original number be $N$. Then $N=9Q_1+8$, and since dividing $Q_1$ by 11 leaves remainder 9, we have $Q_1=11Q_2+9$. Also $Q_2=13Q_3+8$. Substituting step by step, $$ N=9(11Q_2+9)+8=99Q_2+89=99(13Q_3+8)+89=1287Q_3+792+89=1287Q_3+881. $$ So when $N$ is divided by 1287, the remainder is 881. Option A is tempting if the second remainder is copied incorrectly as 8, and C or D can arise from arithmetic slips during substitution.