If a : b = 3 : 4, b : c = 2 : 3, and c : d = 5 : 6, then

Solution

a ∶ b = 3 ∶ 4 b ∶ c = 2 ∶ 3 c ∶ d = 5 ∶ 6 First, make the 'b' term same in both ratios a ∶ b and b ∶ c: a ∶ b = 3 ∶ 4 = 3 × 2 ∶ 4 × 2 = 6 ∶ 8 b ∶ c = 2 ∶ 3 = 2 × 4 ∶ 3 × 4 = 8 ∶ 12 Now, make the 'c' term same in both ratios b ∶ c and c ∶ d: c ∶ d = 5 ∶ 6 = 5 × 3 ∶ 6 × 3 = 15 ∶ 18 Now, combine a ∶ b ∶ c ∶ d: a ∶ b = 6 ∶ 8 b ∶ c = 8 ∶ 12 c ∶ d = 15 ∶ 18 Therefore, a ∶ b ∶ c ∶ d = 6 ∶ 8 ∶ 12 ∶ 15 ∶ 18 ⇒ Simplified: 15 ∶ 20 ∶ 30 ∶ 36