When the positive numbers x, y and z are divided by 31, the remainders are 17, 24 and 27 respectively.When 4x-2y +3z is divided by 31, what will be the remainder?

Correct option is B

Given :

When divided by 31,

x = 31a + 17

y = 31b + 24

z = 31c + 27
where (a, b, c) are positive integers.

Formula Used :

Dividend = (Divisor × Quotient) + Remainder

Solution :

4x - 2y + 3z

Substitute values of (x, y, z):

= 4(31a + 17) - 2(31b + 24) + 3(31c + 27)

= (124a + 68) - (62b + 48) + (93c + 81)

= 31(4a - 2b + 3c) + (68 - 48 + 81)

= 31(4a - 2b + 3c) + 101

Now divide 101 by 31:

101 =$$31 \times 3$$​+ 8
Remainder = 8