y varies inversely with x. If y = 30 when x = 12, find i. y when x =

1.	y varies inversely with x. If y = 30 when x = 12, find i. y when x = 15, ii. x when y = 18.
Answer» Given that, y ∝ (1/x) ∴ y = k x (1/x) where, k is the constant of variation. ∴ y × x = k …(i) When x = 12, y = 30 ∴ Substituting, x = 12 and y = 30 in (i), we get y × x = k ∴ 30 × 12 = k ∴ k = 360 Substituting, k = 360 in (i), we get y × x = k ∴ y × x = 360 ….(ii) i. When x = 15,y = ? ∴ Substituting x = 15 in (ii), we get y × x = 360 ∴ y × 15 = 360 y = 360/15 y = 24 ii. When y = 18, x = ? ∴ Substituting y = 18 in (ii), we get y × x = 360 ∴ 18 × x = 360 x = 360/18 x = 20

y varies inversely with x. If y = 30 when x = 12, find i. y when x = 15, ii. x when y = 18.

Answer»

Given that,

y ∝ (1/x)

∴ y = k x (1/x)

where, k is the constant of variation.

∴ y × x = k …(i)

When x = 12, y = 30

∴ Substituting, x = 12 and y = 30 in (i), we get y × x = k

∴ 30 × 12 = k

∴ k = 360

Substituting, k = 360 in (i), we get y × x = k

∴ y × x = 360 ….(ii)

i. When x = 15,y = ?

∴ Substituting x = 15 in (ii), we get y × x = 360

∴ y × 15 = 360

y = 360/15

y = 24

ii. When y = 18, x = ?

∴ Substituting y = 18 in (ii), we get y × x = 360

∴ 18 × x = 360

x = 360/18

x = 20