In jar A, 120 litres of milk was mixed with 24 litres water. 12 litres of this mixture was taken out and 3 litres of water was added. If 27 litres of newly mixture is taken out, what will be the resultant quantity of water in the jar? (In litre)

Options

A. 20
B. 25
C. 15
D. 19

Answer

To solve the problem step by step, we will follow the sequence of operations described in the question.

### Step 1: Initial Mixture Calculation
In jar A, we have:
- Milk = 120 litres
- Water = 24 litres

Total mixture = Milk + Water = 120 litres + 24 litres = 144 litres.

### Step 2: Ratio of Milk to Water
The ratio of milk to water in the mixture is:
- Milk : Water = 120 : 24 = 5 : 1.

### Step 3: Taking Out 12 Litres of Mixture
When 12 litres of the mixture is taken out, we need to find out how much milk and water is in that 12 litres.

The total parts in the mixture = 5 (milk) + 1 (water) = 6 parts.

Now, each part corresponds to:
- 1 part = 12 litres / 6 = 2 litres.

So, in 12 litres:
- Milk taken out = 5 parts = 5 * 2 = 10 litres.
- Water taken out = 1 part = 1 * 2 = 2 litres.

### Step 4: Remaining Milk and Water After Taking Out
After removing 12 litres (10 litres of milk and 2 litres of water), the remaining quantities are:
- Remaining Milk = 120 litres - 10 litres = 110 litres.
- Remaining Water = 24 litres - 2 litres = 22 litres.

### Step 5: Adding 3 Litres of Water
Next, we add 3 litres of water to the remaining mixture:
- New Water Quantity = 22 litres + 3 litres = 25 litres.

### Step 6: New Mixture Calculation
Now, the new mixture consists of:
- Milk = 110 litres.
- Water = 25 litres.

Total new mixture = 110 litres + 25 litres = 135 litres.

### Step 7: Taking Out 27 Litres of New Mixture
Now, we take out 27 litres of this new mixture. We need to find out how much milk and water is in that 27 litres.

The ratio of milk to water in the new mixture is:
- Milk : Water = 110 : 25.

Total parts = 110 + 25 = 135 parts.

Now, each part corresponds to:
- 1 part = 27 litres / 135 = 0.2 litres.

So, in 27 litres:
- Milk taken out = (110 / 135) * 27 = 22 litres (approximately).
- Water taken out = (25 / 135) * 27 = 5 litres (approximately).

### Step 8: Remaining Milk and Water After Taking Out
After removing 27 litres (22 litres of milk and 5 litres of water), the remaining quantities are:
- Remaining Milk = 110 litres - 22 litres = 88 litres.
- Remaining Water = 25 litres - 5 litres = 20 litres.

### Final Step: Resultant Quantity of Water
The final quantity of water remaining in the jar is:
- 20 litres.

### Answer
The resultant quantity of water in the jar is **20 litres**.

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