Question

12 litres of a milk and water solution having ratio of milk and water as 4 : 1 is mixed with 20 litres of another milk and water solution having ratio of milk and water in the ratio 5 : 1. Find the ratio of milk and water in the resultant solution.

Answer 1

Answer:

The ratio of milk and water in the resultant solution = 197/43

Step-by-step explanation:

Given:

• 12 litres of a milk and water solution having ratio of milk and water as 4 : 1 is mixed with 20 litres of another milk and water solution having ratio of milk and water in the ratio 5 : 1.

To find:

• The ratio of milk and water in the resultant solution.

Solution:

We will multipy volume by their respective ratio and then add them both in case of both milk and water. Then, we will divide the final ratio of milk and final ratio of water to find the ratio of milk and water in the resultant or final solution.

Let's find out...

Resultant ratio = Total milk/Total water

In first case,

12 litres of a milk and water solution having ratio of milk and water as 4 : 1.

In second case,

20 litres of another milk and water solution having ratio of milk and water in the ratio 5 : 1.

In case of milk,

• Milk in first case = 4/5 × 12 ( Total 4 + 1 = 5 )
• Milk in first case = 48/5

• Milk in second case = 5/6 × 20. ( Total 5 + 1 = 6 )
• Milk in second case = 5/3 × 10
• Milk in second case = 50/3

• Total milk = 48/5 + 50/3
• Total milk = (144 + 250)/15
• Total milk = 394/15

Now, in case of water

• Water in first case = 1/5 × 12 ( Total 4 + 1 = 5 )
• Water in first case = 12/5

• Water in second case = 1/6 × 20. ( Total 5 + 1 = 6 )
• Water in second case = 1/3 × 10
• Water in second case = 10/3

• Total water = 12/5 + 10/3
• Total water = (36 + 50)/15
• Total water = 86/15

Finally,

• Resultant ratio = Total milk/Total water
• Resultant ratio = 394/15 ÷ 86/15
• Resultant ratio = 394/15 × 15/86
• Resultant ratio = 394/86. ( Dividing it by 2 )
• Resultant ratio = 197/43

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