m ∝ n, n = 15 when m = 25. Hence i. Find m when n = 87, ii. Find

1.	m ∝ n, n = 15 when m = 25. Hence i. Find m when n = 87, ii. Find n when m = 155.
Answer» Given that, m ∝ n ∴ m = kn …(i) where, k is the constant of variation. When m = 25, n = 15 ∴ Substituting, m = 25 and n = 15 in (i), we get m = kn ∴ 25 = k × 15 ∴ k = 25/15 ∴ k = 5/3 Substituting k = 5/3 in (i), we get m = kn ∴ m = (5/3)n ... (ii) i. When n = 87, m = ? Substituting n = 87 in (ii), we get m = (5/3)n m = (5/3) x 87 m = 5 × 29 m = 145 ii. When m = 155, n = ? ∴ Substituting m = 155 in (ii), we get m = (5/3)n ∴ 155 = (5/3)n ∴ (155 x 3)/5 = n ∴ n = 31 × 3 ∴ n = 93

m ∝ n, n = 15 when m = 25. Hence i. Find m when n = 87, ii. Find n when m = 155.

Answer»

Given that, m ∝ n

∴ m = kn …(i) where, k is the constant of variation.

When m = 25, n = 15

∴ Substituting, m = 25 and n = 15 in (i), we get m = kn

∴ 25 = k × 15

∴ k = 25/15

∴ k = 5/3

Substituting k = 5/3 in (i), we get m = kn

∴ m = (5/3)n ... (ii)

i. When n = 87, m = ?

Substituting n = 87 in (ii), we get m = (5/3)n

m = (5/3) x 87

m = 5 × 29

m = 145

ii. When m = 155, n = ?

∴ Substituting m = 155 in (ii), we get m = (5/3)n

∴ 155 = (5/3)n

∴ (155 x 3)/5 = n

∴ n = 31 × 3

∴ n = 93