There are two mixtures of honey and water in which the ratio of honey and water are as 1:3 and 3:1 respectively. Two litres are drawn from first mixture and 3 litres from second mixture, are mixed to form another mixture. What is the ratio of honey and water in it?

Step 1: Understand the composition of the two mixtures

• Mixture 1: Ratio of honey to water = 1:3
• This means for every 4 parts, 1 part is honey and 3 parts are water.
• Mixture 2: Ratio of honey to water = 3:1
• This means for every 4 parts, 3 parts are honey and 1 part is water.

Step 2: Quantities drawn from each mixture

• From Mixture 1: 2 litres
• Honey in Mixture 1 = (1/4) × 2 = 0.5 litres
• Water in Mixture 1 = (3/4) × 2 = 1.5 litres

• From Mixture 2: 3 litres
• Honey in Mixture 2 = (3/4) × 3 = 2.25 litres
• Water in Mixture 2 = (1/4) × 3 = 0.75 litres

Step 3: Combine the two extracted mixtures

• Total honey = 0.5 (from Mixture 1) + 2.25 (from Mixture 2) = 2.75 litres
• Total water = 1.5 (from Mixture 1) + 0.75 (from Mixture 2) = 2.25 litres

Step 4: Find the ratio of honey to water in the final mixture

Honey : Water = 2.75 : 2.25
              = 275 : 225
              = 11 : 9

Answer: 11 : 9

After mixing 2 litres from the 1:3 honey-water mixture and 3 litres from the 3:1 mixture, the final ratio of honey to water becomes 11:9.

This problem is an excellent example of how mixtures and proportions can be handled using basic arithmetic and ratio concepts. It often appears in competitive exams and aptitude tests, especially in sections related to quantitative aptitude. Understanding this kind of question helps strengthen your grip on real-life applications of mathematics, such as preparing mixtures, blending solutions, or even calculating nutrient percentages in food science. These types of questions are popular in exams like SSC, IBPS, CAT, and other government or management entrance tests.