The ratio of water and milk in a mixture of 65 litre is `5 : 8`. What quantity of water (in litre) must be added so that the ratio of water and milk becomes `3 : 4` ?

Options

A. A)3 litres
B. B)4 litres
C. C)5 litres
D. D)6 litres

Answer

To solve the problem step by step, we need to find out how much water must be added to change the ratio of water to milk from 5:8 to 3:4 in a 65-liter mixture.

### Step 1: Determine the initial quantities of water and milk.
The total mixture is 65 liters, and the ratio of water to milk is 5:8.

- The total parts in the ratio = 5 + 8 = 13 parts.
- Quantity of water = (5/13) * 65 = 25 liters.
- Quantity of milk = (8/13) * 65 = 40 liters.

**Hint:** To find the individual quantities from a ratio, divide the total quantity by the sum of the ratio parts and multiply by the respective ratio part.

### Step 2: Set up the new ratio after adding water.
We need to find out how much water (let's call it 'x' liters) needs to be added so that the new ratio of water to milk becomes 3:4.

- New quantity of water = 25 + x liters.
- Quantity of milk remains the same = 40 liters.

### Step 3: Write the equation based on the new ratio.
According to the new ratio of water to milk (3:4):

\[ \frac{25 + x}{40} = \frac{3}{4} \]

### Step 4: Cross-multiply to solve for 'x'.
Cross-multiplying gives us:

\[ 4(25 + x) = 3(40) \]

Expanding both sides:

\[ 100 + 4x = 120 \]

### Step 5: Isolate 'x' and solve.
Now, we isolate 'x':

\[ 4x = 120 - 100 \]
\[ 4x = 20 \]
\[ x = \frac{20}{4} = 5 \]

### Conclusion:
The quantity of water that must be added is **5 liters**.

### Final Answer:
5 liters.

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