A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13?

Let the number be a.

By Euclid’s division lemma -

Putting the values of divisor as 143 and remainder as 31.

a = 143(q) + 31, where q is the quotient when divided by 143.

a = {13(11)}q + 31

a = 13(11)q + 13(2) + 5.

a = 13(11q + 2) + 5 - (i)

Again when it is divided by 13, let the remainder be r.

So, a = 13(p) + r - (ii), where p is the quotient when divided by 13.

Comparing (i) and (ii) -

11q + 2 = p and r = 5.

So remainder = 5.