Kulbhushan started a juice (syrup + water) counter. Initially, he had 140 litres of juice which had 40% water in it. He sold 30 litres of the juice. Then he added equal amounts of of syrup and water. Now the ratio of water to syrup became 3:4. What quantity of water was added?

Options

A. 24 litres
B. 28 litres
C. 26 litres
D. 22 litres

Answer

To solve the problem step by step, we will break it down into manageable parts:

### Step 1: Calculate the initial amount of water and syrup in the juice.
- **Total juice = 140 liters**
- **Water percentage = 40%**
- **Water in juice = 40% of 140 liters = 0.4 × 140 = 56 liters**
- **Syrup in juice = Total juice - Water = 140 - 56 = 84 liters**

### Step 2: Determine the amount of juice sold and the remaining amounts.
- **Juice sold = 30 liters**
- Since the juice has the same ratio of water and syrup, we need to find the amount of water and syrup in the 30 liters sold.
- **Water in sold juice = 40% of 30 liters = 0.4 × 30 = 12 liters**
- **Syrup in sold juice = 30 liters - 12 liters = 18 liters**

### Step 3: Calculate the remaining amounts after selling the juice.
- **Remaining water = Initial water - Water sold = 56 - 12 = 44 liters**
- **Remaining syrup = Initial syrup - Syrup sold = 84 - 18 = 66 liters**
- **Remaining juice = Total juice - Juice sold = 140 - 30 = 110 liters**

### Step 4: Add equal amounts of syrup and water.
Let the amount of syrup and water added be \( y \) liters each.
- **New amount of water = Remaining water + Water added = 44 + y liters**
- **New amount of syrup = Remaining syrup + Syrup added = 66 + y liters**

### Step 5: Set up the ratio of water to syrup.
According to the problem, the new ratio of water to syrup is 3:4.
- This can be expressed as:
\[ \frac{44 + y}{66 + y} = \frac{3}{4} \]

### Step 6: Cross-multiply to solve for \( y \).
Cross-multiplying gives:
\[ 4(44 + y) = 3(66 + y) \]
Expanding both sides:
\[ 176 + 4y = 198 + 3y \]

### Step 7: Rearranging the equation to isolate \( y \).
Subtract \( 3y \) from both sides:
\[ 176 + 4y - 3y = 198 \]
This simplifies to:
\[ 176 + y = 198 \]
Now, subtract 176 from both sides:
\[ y = 198 - 176 = 22 \]

### Step 8: Conclusion
The quantity of water added is \( y = 22 \) liters.

### Final Answer
**The quantity of water added is 22 liters.**

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