Question

On dividing a number by 19, the difference between quotient and remainder is 9. The number is

Answer 1

On dividing a number by 19, the difference between quotient and remainder is 9. The number is 371

Solution:

Let the number be N

Let the remainder be x

Let the quotient be Q

Given that,

The difference between quotient and remainder is 9

Q - x = 9

Q = 9 + x

Then,

$Number = divisor \times quotient + remainder\\\\Number = 19 \times (9+x) + x\\\\Number = 171+19+x\\\\Number = 171+20x$

N = 171 + 20x

Therefore, the number must be 371

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