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Question : Two numbers, when divided by a certain divisor, leave the remainder 57. When the sum of the two numbers is divided by the same divisor, the remainder is 49. The divisor is:

Option 1: 56

Option 2: 57

Option 3: 49

Option 4: 65


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 17th Jan, 2024

Correct Answer: 65


Solution : Let the two numbers be $a$ and $b$ and the divisor is $d$.
According to the question,
$a = d×p + 57$ and $b=d×q + 57$, where $p$ and $q$ are the quotients.
Adding these two equations we get,
$(a+b)=d(p+q)+114$
Again when the sum of the two numbers is divided by the same divisor, the remainder is 49.
$\therefore$ Divisor = (114 – 49) = 65
Hence, the correct answer is 65.

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