x varies inversely as y, when x = 15 then y = 10, if x = 20, then y =

1.	x varies inversely as y, when x = 15 then y = 10, if x = 20, then y = ?
Answer» Given that x ∝ (1/√y) x = k × (1/√y) where, k is the constant of variation. ∴ x × y = k …(i) When x = 15, y = 10 ∴ Substituting, x = 15 and y = 10 in (i), we get x × y = k ∴ 15 × 10 = k ∴ k = 150 Substituting, k = 150 in (i), we get x × y = k ∴ x × y = 150 …(ii) This is the equation of variation. When x = 20, y = ? ∴ substituting x = 20 in (ii), we get x × y = 150 ∴ 20 × y = 150 ∴ y = 150/20 ∴ y = 7.5

x varies inversely as y, when x = 15 then y = 10, if x = 20, then y = ?

Answer»

Given that

x ∝ (1/√y)

x = k × (1/√y)

where, k is the constant of variation.

∴ x × y = k …(i)

When x = 15, y = 10

∴ Substituting, x = 15 and y = 10 in (i), we get

x × y = k

∴ 15 × 10 = k

∴ k = 150

Substituting, k = 150 in (i), we get

x × y = k

∴ x × y = 150 …(ii)

This is the equation of variation.

When x = 20, y = ?

∴ substituting x = 20 in (ii), we get x × y = 150

∴ 20 × y = 150

∴ y = 150/20

∴ y = 7.5