Question

IF TWO NUMBERS WHEN DIVIDED BY A CERTAIN DIVISOR GIVE REMAINDER 35 AND 30 RESPECTIVELY AND WHEN THEIR SUM IS DIVIDED BY THE SAME DIVISOR,THE REMAINDER IS 20,THEN THE DIVISOR IS -
(A)40 (B) 45 (C) 50 (D) 55
GIVE XPLANATION

Answer 1

Answer:

Let the certain divisor be x and quotients obtained in two cases are y and z leaving remainders 30 and 35 So first number is x(y) +30 and second number is x(z) +35 Hence sum of these two numbers is x(y+z) +65 .

It is given that when sum of these numbers is divided by x it leaves a remainder 20 So We know that x(y+z) is divisible by x Hence

65 when divided by x leaves remainder 20 so x => 65-20 => 45 . 45 is the answer.

Answer 2

Let the two numbers be x and y and the required divisor be n.

So applying Euclid's Division algorithm we get,

x = ap + 35.....(1)

y = aq + 30......(2)

(x+y) = ar + 20.......(3)

Now add (1) and (2),

(x+y) = a(p+q) + 95.....(4)

Equate (3) and (4),

a(p+q) +95 = ar+20

a(r-p-q) = 45

Taking x and y as smallest number i.e, 1,

r-p-q = 1

Thus a = 45