Question

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

(a) 0
(b) 1
(c) 3
(d) 5

Answer 1

(d) 5

We know,
Dividend = Divisor $\times$ Quotient + Remainder.
It is given that:
Divisor = 143
Remainder = 13
So, the given number is in the form of 143x + 31, where x is the quotient.
∴ 143x + 31 = 13 (11x) + (13 $\times 2$) + 5 = 13 (11x + 2) + 5
Thus, the remainder will be 5 when the same number is divided by 13.