If two numbers, when divided by a divisor, gives remainder 35 and 30 respectively and when their sum is divided by the same divisor, the remainder is 20, then the divisor is:

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If two numbers, when divided by a divisor, gives remainder $35 and 30$ respectively and when their sum is divided by the same divisor, the remainder is $20,$ then the divisor is:

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answer is B.

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Detailed Solution

Concept: To express the numbers in terms of their divisor, quotient, and remainder, use the Euclid division lemma.
Let x and y, respectively, be the starting points for the inquiry. Additionally, make p the divisor.
The equation

s = tq + r,

such that r is positive and less than

q,

is always true for two integers s and t, according to Euclid's Division Lemma.
The numbers can be expressed as follows

: x = pk + 35 . . . . . . . . . . . . . . . . . (i)

y = pl + 30 \dots \dots \dots \dots \dots . . (ii)

Positive natural integers, k and l, are used in the equations above. Now that a condition on the sum of the two integers is stated in the question, we will add the two equations.