Question

85 litres of a mixture contain milk and water in the ratio 27:7. How much water is required to be added so that the resulting mixture contains milk and water in the ratio 3:1?

• A. 6 L
• B. 8 L
• C. 4 L
• D. 5 L

Hint:

In mixture problems, remember that when only one component is added, the quantity of the other component remains constant. Use this fact to form ratios easily.

Answer 1

The Correct Option is D

Step 1: Understand the given ratio of milk and water.
The ratio of milk to water in the mixture is given as 27 : 7.
The total parts of the mixture are:
\[ 27 + 7 = 34 \]
Step 2: Find the quantity of milk and water in the mixture.
Total mixture = 85 litres.
Milk in the mixture is:
\[ \frac{27}{34} \times 85 = 67.5 \text{ litres} \]
Water in the mixture is:
\[ \frac{7}{34} \times 85 = 17.5 \text{ litres} \]
Step 3: Note that only water is added.
When water is added, the quantity of milk remains unchanged.
Milk will remain equal to 67.5 litres.
Step 4: Use the new ratio of milk and water.
The required final ratio of milk to water is 3 : 1.
This means water must be one-third of the milk quantity.
Step 5: Find the required final quantity of water.
\[ \text{Required water} = \frac{1}{3} \times 67.5 = 22.5 \text{ litres} \]
Step 6: Find the amount of water to be added.
Initially, water = 17.5 litres.
Final water required = 22.5 litres.
\[ \text{Water to be added} = 22.5 - 17.5 = 5 \text{ litres} \]
Step 7: Final conclusion.
Hence, the amount of water required to be added is 5 litres.