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Q.


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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a

40

b

45

c

50

d

55 

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 ……………..(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.
pk + pl + 65 = x + y = pn + 65
The equation becomes x + y = pn + p + 20 since the residual should be 20, as shown in the question.
We can therefore conclude that p+20 is equivalent to 65 based on the aforementioned findings. Mathematically, we obtain p+20=65 and p=45.
As a result, option is the response to the above question because the divisor is 45.
Hence, the correct option is 2) .
 ExamType: CBSE
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