How much chicory at Rs.24 a kg should be added to 15 kg of tea at Rs.60 a kg as to make the mixture worth Rs.39 a kg ?

Options

A. 21 kg
B. 20 kg
C. 27 kg
D. 18 kg

Answer

To solve the problem of how much chicory at Rs. 24 per kg should be added to 15 kg of tea at Rs. 60 per kg to make the mixture worth Rs. 39 per kg, we can use the method of alligation. Here are the step-by-step calculations:

### Step 1: Identify the given values
- Cost of tea (C1) = Rs. 60 per kg
- Cost of chicory (C2) = Rs. 24 per kg
- Mean cost of the mixture (CP) = Rs. 39 per kg
- Quantity of tea = 15 kg

### Step 2: Set up the alligation
Using the alligation method, we can set up the following:

```
C1 (Tea) = Rs. 60
CP (Mixture) = Rs. 39
C2 (Chicory) = Rs. 24
```

### Step 3: Calculate the differences
- Difference between C1 and CP:
\[ C1 - CP = 60 - 39 = 21 \]
- Difference between C2 and CP:
\[ CP - C2 = 39 - 24 = 15 \]

### Step 4: Write the ratio
The ratio of the quantities of chicory to tea can be determined from the differences calculated:
\[ \text{Ratio} = \frac{C1 - CP}{CP - C2} = \frac{21}{15} \]
This simplifies to:
\[ \frac{7}{5} \]

### Step 5: Calculate the quantity of chicory
Let the quantity of chicory to be added be \( x \) kg. According to the ratio, we have:
\[ \frac{x}{15} = \frac{7}{5} \]
Cross-multiplying gives:
\[ 5x = 7 \times 15 \]
\[ 5x = 105 \]
\[ x = \frac{105}{5} = 21 \text{ kg} \]

### Conclusion
Therefore, the amount of chicory that should be added is **21 kg**.

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