i. p ∝ (1/q) … [Given] 

∴ p = k × (1/q) where, k is the constant of variation. 

∴ p × q = k …(i) 

When p = 15, q = 4 

∴ Substituting p = 15 and q = 4 in (i), we get

p × q = k 

∴ 15 × 4 = k 

∴ k = 60 

Substituting k = 60 in (i), we get p × q = k 

∴ p × q = 60 

This is the equation of variation. 

∴ The constant of variation is 60 and the equation of variation is pq = 60.

ii. z ∝ (1/w) …[Given] 

∴ z = k × (1/w) where, k is the constant of variation, 

∴ z × w = k …(i) 

When z = 2.5, w = 24 

∴ Substituting z = 2.5 and w = 24 in (i), we get 

z × w = k 

∴ 2.5 × 24 = k 

∴ k = 60

Substituting k = 60 in (i), we get z × w = k 

∴ z × w = 60 

This is the equation of variation. 

∴ The constant of variation is 60 and the equation of variation is zw = 60.

iii. s ∝ (1/t²) …[Given]

∴ s = k x (1/t²)

∴ where, k is the constant of variation, 

∴ s × t² = k …(i) 

When s = 4, t = 5 

∴ Substituting, s = 4 and t = 5 in (i), we get 

s × t² = k 

∴ 4 × (5)² = k 

∴ k = 4 × 25 

∴ k = 100 

Substituting k = 100 in (i), we get s × t² = k

∴ s × t² = 100 

This is the equation of variation. 

∴ The constant of variation is 100 and the equation of variation is st² = 100.

iv. x ∝ (1/√y) …[Given] 

∴ x = k x (1/√y) where, k is the constant of variation, 

∴ x × √y = k …(i) 

When x = 15, y = 9 

∴ Substituting x = 15 and y = 9 in (i), we get 

x × √y = k 

∴ 15 × √9 = k 

∴ k = 15 × 3 

∴ k = 45 

Substituting k = 45 in (i), we get 

x × √y = k 

∴ x × √y = 45. 

This is the equation of variation.

∴ The constant of variation is k = 45 and the equation of variation is x√y = 45.