Question

When two numbers are separately divided by 33, the remainders are 21 and 28 respectively. If the sum of the two numbers is divided by 33, then find the remainder.

Answer 1

Let the numbers be a & b.

$\frac{a}{33}=p\left(33\right)+21$

$\frac{b}{33}=q\left(33\right)+28$

Where $p\left(33\right)$, $q\left(33\right)$ are multiples of $33$ & hence the quotient.

$\frac{(a+b)}{33}=p\left(33\right)+21+q\left(33\right)+28$

$\frac{(a+b)}{33}=33(p+q)+49$

$\frac{a+b}{33}=33(p+q)+33+16$

$\frac{a+b}{33}=33(p+q+1)+16$

Hence the remainder is $16$.