Dealing with Remainders

Note for remainder problems:

x = q*y + r

x => Dividend or Multiple
q => Quotient
y => Divisor or Factor
r => Remainder ( 0<= r < q )
All the numbers in the equation above are integers.

If x is divisible by y then the remainder r is 0.


Solution to the problem:

We know that x is not divisible y because we have a remainder of 9. Lets set up the remainder equation:

x = n.y + r
x = n.y + 9
(x/y) = n + (9/y) ..... (1) Dividing both sides by integer y

But its given that,
(x/y) = 96.12
(x/y) = 96 + 0.12 ..... (2) Splitting into integer and decimal parts

Now, Comparing (1), (2)
(9/y) = 0.12
Thus y = (9/0.12) = 75

[spoiler]Correct Answer : B[/spoiler]

.12y = 9

y = 75

Answer [spoiler]{B}[/spoiler]