The allowance provided in between a hole and a shaft is calculated from the difference between

The correct option is: "upper limit of the shaft and the lower limit of the hole ".

Understanding Allowance in Metrology:
In engineering and manufacturing, "allowance" is the intentional, desired difference between the dimensions of mating parts (specifically, a hole and a shaft) to achieve a specific class of fit (such as a clearance fit or interference fit). It represents the tightest possible fit between the two mating parts.

Step-by-Step Derivation of the Allowance Calculation:
To find the tightest possible fit (which defines the allowance), we must pair the largest possible shaft with the smallest possible hole:
1. The largest permissible size of the shaft is its upper limit (maximum material condition of the shaft).
2. The smallest permissible size of the hole is its lower limit (maximum material condition of the hole).

Thus, the allowance is mathematically defined as the algebraic difference between these two specific limits:
$$\text{Allowance}=\text{Lower limit of hole}-\text{Upper limit of shaft}$$
This directly corresponds to the difference between the upper limit of the shaft and the lower limit of the hole.