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:

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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:

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answer is B.

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Detailed Solution

Concept- Using Euclid division lemma to write the number in terms of its division, quotient, and remainder.
Let the number be

x

and

y

respectively, and the divisor be

p .

So, the numbers can be written as:

x = pk + 35

……………………..(i)

y = pl + 30

……………………..(ii)

k

and

l

are positive natural numbers, we will add both the equations according to the given condition, we get

\Rightarrow x + y = pk + pl + 65

\Rightarrow x + y = pn + 65

Given in the question that remainder should be 20, we get

\Rightarrow x + y = pm + p + 20

Therefore, from the above results, we get

p + 20 = 65

\Rightarrow p = 45

Therefore, the divisor is 45.
Hence, the correct answer is option 2.

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