Question

A quantity P is partly varies inversely as a quantity Q. Given that P=10 when Q=1.5 and P=20 when Q=1.25. Find the equation connecting P and Q

Answer 1

not sure just what "A quantity P is partly varies inversely" means, but let's go with
p = a + k/q
Now, to find a and k, just use the given values, and solve
a + k/1.5 = 10
a + k/1.25 = 20

Answer 2

Assuming you have a typo and you meant:
"A quantity P is partly constant and varies inversely as a quantity Q"

P = c + k/Q

when P=10, Q = 1.5
10 = c + k/1.5
times 3 ----> 30 = 3c + 2k **

when P = 20, Q = 1.25 or 5/4
20 = c + k/(5/4)
times 20 ----> 400 = 20c + 16k or 100 = 5c + 4k ***

I will assume you can solve these two equations for c and k,
then form the equation P = c + k/Q

let me know what you get.