When a number is divided by a divisor, the remainder is 16. When twice the original number is divided by the same divisor, the remainder is 3. Find the value of that divisor.

Correct option is A

Given:

When a number N is divided by a divisor D, the remainder is 16.

When twice the original number 2N is divided by the same divisor D, the remainder is 3

Formula used:

Dividend=Divisor×Quotient+Remainder

Solution:

Let the original number be a

Let the divisor be d

Let the quotient of dividing a by d be x

According to the question

a= dx +16

Twice the original number is divided by d means 2a is divided by d

2a = 2dx +32

​When 2(dx+16) is divided by d, the remainder is 3

2dx is perfectly divisible by d and will therefore, not leave a remainder.

The remainder of 3 was obtained by dividing 32 by d:

2a=2(dx+16) = 2dx+32

So, 32mod d=3

32−3=29

Therefore, d=29

The value of the divisor is 29.​