Given: First : second = 2 : 3 Second : third = 6 : 5 First × third = 1620 Calculation: Let third is = 5m Second = 6m First = 6m/3 × 2 ⇒ 4m First × third = 1620 ⇒4m×5m=1620 ⇒20m2=1620 ⇒m2=81 ⇒ m = 9 First = 4m ⇒ 4 × 9 ⇒ 36 Second = 6m ⇒ 6 × 9 ⇒ 54 Third = 5m ⇒ 5 × 9 ⇒ 45 Difference between second and third = 54 — 45 ⇒ 9 Let us combine the two ratios to get one single ratio between first, second, and third numbers. Ratio between first and second number × 2 = 4 ∶ 6 Now combining the two ratios we get, first ∶ second ∶ third = 4 ∶ 6 ∶ 5 Product of first and third = 4 unit × 5 unit = 1620 1 unit = √(1620/20) = 9 Difference between second and third number = 6 unit - 5 unit = 1 unit = 9 ∴ The required difference is 9.