To solve this problem, we need to use the concept of division and remainders. Let's break down the given information and solve step by step:

Given:
- x/y = 96.12
- Remainder when x is divided by y = 9

Step 1: Understanding the Remainder Concept
When we divide a positive integer x by a positive integer y, the remainder is the amount left over after dividing as many whole y's as possible. For example, if we divide 10 by 3, the remainder is 1 because 3 goes into 10 three times (3 * 3 = 9) and there is 1 left over.

Step 2: Expressing the Decimal as a Fraction
The given x/y = 96.12 can be expressed as a fraction by removing the decimal point:
x/y = 96.12 = 9612/100

Step 3: Expressing the Fraction in Terms of Remainder
When we divide 9612 by 100, we can express it as:
9612 = 100 * 96 + 12

Step 4: Equating Remainders
Since the remainder when x is divided by y is given as 9, we can equate the remainder with the remainder obtained from the expression in step 3:
12 = 9

Step 5: Finding the Value of y
To find the value of y, we need to determine the divisor that gives a remainder of 9 when dividing any multiple of 100. In other words, we need to find a number that leaves a remainder of 9 when divided by y.

Let's check the answer choices:
a) 96: 100 divided by 96 gives a remainder of 4, not 9
b) 75: 100 divided by 75 gives a remainder of 25, not 9
c) 48: 100 divided by 48 gives a remainder of 4, not 9
d) 25: 100 divided by 25 gives a remainder of 0, not 9

Therefore, none of the answer choices satisfies the condition.

It seems there may be an error in the answer choices, as none of them provide the correct value of y.

96.12=96.12/100=96.3/25=y=75