Number Problem
Number Theory
Level
pending
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
The answer is 37.
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1 solution
Let the original number be 'a' Let the divisor be 'd'
Let the quotient of the division of a by d be 'x'
Therefore, we can write the relation as a d =x and the remainder is 24. i.e., a=dx+24
When twice the original number is divided by d, 2a is divided by d. We know that a=dx+24. Therefore, 2a=2dx+48
The problem states that
(2dx+48) d leaves a remainder of 11. 2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d. When 48 is divided by 37, the remainder that one will obtain is 11. Hence, the divisor is 37.