A vessel contains milk and water in the ratio of 4:3. If 14 litres of the mixture is drawn and filled with water, the ratio changes to 3:4. How much milk was there in the vessel initially?a)24b)32c)40d)48e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Answer – b) 32 Explanation : milk = 4x and water = 3x milk = 4x – 14*4/7 and water = 3x – 14*3/7 + 14 4x – 8: 3x + 8 = 3:4 X = 8, so milk = 8*4 = 32 litres

Answer

Given:

- Ratio of milk and water in the vessel = 4:3
- 14 litres of mixture is drawn and filled with water
- New ratio of mixture = 3:4

To find: Initial quantity of milk in the vessel

Let's assume that the initial quantity of milk and water in the vessel is 4x and 3x respectively.

Step 1: Calculation of initial quantity of mixture in the vessel

- Ratio of milk and water in the vessel = 4:3
- Let the common ratio be 'k'
- So, 4x + 3x = 7x = k
- Therefore, the initial quantity of mixture in the vessel = 7x

Step 2: Calculation of quantity of mixture drawn

- Quantity of mixture drawn = 14 litres

Step 3: Calculation of quantity of water added

- Quantity of mixture drawn is replaced by water
- So, the quantity of water added = 14 litres

Step 4: Calculation of quantity of mixture left in the vessel

- Initial quantity of mixture = 7x
- Quantity of mixture drawn = 14 litres
- Quantity of water added = 14 litres
- Therefore, the quantity of mixture left in the vessel = 7x - 14 + 14 = 7x

Step 5: Calculation of new ratio of milk and water in the vessel

- Quantity of milk left in the vessel = 4x
- Quantity of water left in the vessel = 3x + 14
- New ratio of milk and water in the vessel = (4x)/(3x+14) = 3/4

Step 6: Calculation of initial quantity of milk in the vessel

- Solving the equation (4x)/(3x+14) = 3/4
- We get, x = 8
- Therefore, the initial quantity of milk in the vessel = 4x = 32 litres

Hence, option (B) is the correct answer.

Similar Quant Doubts

The diluted Milk contains only 8 liters of Milk and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing Milk. How many liters of the mixture shall be replaced with pure Milk if there was initially 32 liters of water in the mixture?

A vessel contains a mixture of two liquids A and B in the ratio of 4:1. When 10 litres of the mixture is replaced with liquid B, the ratio becomes 2:3. How many litres of liquid A was present in the jar initially?

A bucket contains a mixture of two liquids A and B in the proportion 5: 7 . If 6 litres of the mixture is replaced by 6 litres of liquid B, then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the Bucket initially?

Top Courses for Quant

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company