To solve this problem, we can use the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases and vice versa.
Let's denote the constant part of the quantity p as k.
We are given that p is partly constant and partly varies inversely as q, and we have two sets of values for p and q:
When q = 1.5, p = 10.
When q = 1.25, p = 20.
Using the concept of inverse variation, we can express the relationship between p and q as:
p = k/q
Now, we can solve for the value of k. Let's substitute the values from the first set of values:
10 = k/1.5
To isolate k, we can multiply both sides of the equation by 1.5:
10 * 1.5 = k
15 = k
Now that we have the value of k, we can substitute it into the equation to find the value of p when q = 0.5:
p = 15/0.5
p = 30
Therefore, when q = 0.5, the value of p is 30.