Question

A number when divided by 627 leaves a
remainder 43. By dividing the same
number by 19, the remainder will be

(a) 24 (b) 43
(b) 43 (C) 13 (d) 5
(e) 7​

Answer 1

Step-by-step explanation:

We know that dividend = divisor \times× quotient + remainder

Let the dividend number required be x.

When x is divided by 627, the remainder is 43.

x = 627k + 43

Where,

k is the quotient

627 is the divisor

43 is remainder.

Here, x is the multiple of 627

Let us consider the factors of 627

627 = 3 \times 209 = 3 \times 19 \times 11627=3×209=3×19×11

Expressing the equation in terms of 19 would help to solve the problem, as we need to find the remainder when x is divided by 19.

As 43 = 38 + 5 = 19 \times× 2 + 5

Therefore,

x = 19 \times 3 \times 11 \times k + (19 \times 2 + 5)x=19×3×11×k+(19×2+5)

x = 19(33k + 2) + 5

This is in the form of dividend, divisor, quotient, and remainder.

This means that x when divided by 19 with divisor 33k + 2, gives remainder 5.

Therefore, the remainder is 5 when the same number is divided by 19.