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A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?

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Calculation

Solution Quantity = 40 litres

⇒ Ratio of dye and water = 2 : 3

⇒ Dye = 16 litres and water = 24 litres

⇒ New ratio = 2 : 5

⇒ dye remains same = 16 litres

⇒ Water = 24 + 16 = 40 litres

⇒ When 1/4 mixture removes

⇒ Dye = 12 litres and water = 30 litres

⇒ Now ratio becomes 2 : 3

⇒ 3 unit = 30

⇒ 1 unit = 10

⇒ 2 unit = 20 litres

⇒ 20 - 12 = 8 litres

⇒ 8 litres extra dye is added

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