How many bananas at 5 for Rs.1.20 should be mixed with 300 bananas at 6 for Rs.2.10, so that they should all be worth Rs.3.60 a dozen ?

Options

A. 350
B. 280
C. 320
D. 250

Answer

To solve the problem of how many bananas priced at 5 for Rs. 1.20 should be mixed with 300 bananas priced at 6 for Rs. 2.10, so that the total mixture is worth Rs. 3.60 a dozen, we can follow these steps:

### Step 1: Determine the cost per banana for each type
- **Cost of bananas at 5 for Rs. 1.20**:
\[ \text{Cost per banana} = \frac{1.20}{5} = 0.24 \text{ Rs.} \]

- **Cost of bananas at 6 for Rs. 2.10**:
\[ \text{Cost per banana} = \frac{2.10}{6} = 0.35 \text{ Rs.} \]

### Step 2: Determine the cost per dozen for each type
- **Cost per dozen for bananas at 5 for Rs. 1.20**:
\[ \text{Cost per dozen} = 0.24 \times 12 = 2.88 \text{ Rs.} \]

- **Cost per dozen for bananas at 6 for Rs. 2.10**:
\[ \text{Cost per dozen} = 0.35 \times 12 = 4.20 \text{ Rs.} \]

### Step 3: Determine the cost per dozen for the desired mixture
- **Desired cost per dozen**:
\[ \text{Desired cost per dozen} = 3.60 \text{ Rs.} \]

### Step 4: Use the allegation method
Using the allegation method, we can set up the following:

- Higher price (Cost of 6 for Rs. 2.10): Rs. 4.20
- Lower price (Cost of 5 for Rs. 1.20): Rs. 2.88
- Mean price (Desired price): Rs. 3.60

Now, we calculate the differences:
- Difference between higher price and mean price:
\[ 4.20 - 3.60 = 0.60 \]
- Difference between mean price and lower price:
\[ 3.60 - 2.88 = 0.72 \]

### Step 5: Set up the ratio
The ratio of the quantities of the two types of bananas is given by the differences calculated:
\[ \text{Ratio} = \frac{0.60}{0.72} = \frac{60}{72} = \frac{5}{6} \]

### Step 6: Calculate the number of bananas needed
Let \( x \) be the number of bananas at 5 for Rs. 1.20. According to the ratio, we have:
\[ \frac{x}{300} = \frac{5}{6} \]

Cross-multiplying gives:
\[ 6x = 5 \times 300 \]
\[ 6x = 1500 \]
\[ x = \frac{1500}{6} = 250 \]

### Conclusion
Therefore, the number of bananas at 5 for Rs. 1.20 that should be mixed is **250**.

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