correct answer is: b) 0.05 kg

Explanation

To find the required greatest quantity we need to find the HCF of the given quotients.
Here, given quantities are 8.15 kg, 10.25 kg and 12.75 kg.
Let,
8.15 kg = 815 kg
10.25 kg = 1025 kg
12.75 kg = 1275 kg
So, HCF of 815 kg, 1025 kg and 1275 kg is = 5 kg
So that, HCF of 8.15 kg, 10.25 kg and 12.75 kg is = 0.05 kg _{[2 digits after decimal point]}
\therefore 0.05 kg is the greatest quantity by which 8.15 kg 10.25 kg, and 12.75 kg must be divided so that the quotients are integers.
Ans: 0.05 kg is the greatest quantity.

Another method to articulate this particular math query is available:

1. What is the largest amount by which 8.15 kg, 10.25 kg, and 12.75 kg must be divided to yield integer quotients?
2. By what largest quantity can 8.15 kg, 10.25 kg, and 12.75 kg be divided to produce integers as quotients?
3. Identify the greatest divisor that ensures 8.15 kg, 10.25 kg, and 12.75 kg are divisible, giving integer quotients.
4. Determine the greatest divisor that makes 8.15 kg, 10.25 kg, and 12.75 kg divisible with integer results.
5. Find the maximum quantity that divides 8.15 kg, 10.25 kg, and 12.75 kg evenly, resulting in whole numbers.