The ratio of spirit and water in | two mixturers of 20 litre and 36 litre is 3:7 and 7:5 respective ly. Both the mixtures are mixed together. Now the ratio of the spirit and water in the new mix ture is

Options

A. `25:29`
B. `9:10`
C. `27:29`
D. `27:31`

Answer

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

### Step 1: Understand the Ratios and Volumes
We have two mixtures:
- Mixture 1: 20 liters with a spirit to water ratio of 3:7
- Mixture 2: 36 liters with a spirit to water ratio of 7:5

### Step 2: Calculate the Amounts in Mixture 1
For Mixture 1 (20 liters, ratio 3:7):
- Total parts = 3 + 7 = 10 parts
- Each part = Total volume / Total parts = 20 liters / 10 = 2 liters

Now, calculate the amounts of spirit and water:
- Spirit = 3 parts = 3 * 2 = 6 liters
- Water = 7 parts = 7 * 2 = 14 liters

### Step 3: Calculate the Amounts in Mixture 2
For Mixture 2 (36 liters, ratio 7:5):
- Total parts = 7 + 5 = 12 parts
- Each part = Total volume / Total parts = 36 liters / 12 = 3 liters

Now, calculate the amounts of spirit and water:
- Spirit = 7 parts = 7 * 3 = 21 liters
- Water = 5 parts = 5 * 3 = 15 liters

### Step 4: Combine the Mixtures
Now, we combine both mixtures:
- Total Spirit = Spirit from Mixture 1 + Spirit from Mixture 2 = 6 liters + 21 liters = 27 liters
- Total Water = Water from Mixture 1 + Water from Mixture 2 = 14 liters + 15 liters = 29 liters

### Step 5: Find the New Ratio
The new ratio of spirit to water in the combined mixture is:
- Ratio = Total Spirit : Total Water = 27 liters : 29 liters

### Final Answer
The ratio of spirit to water in the new mixture is **27:29**.

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