Currants at Rs. 50 per kg are mixed with currants at Rs. 90 per kg to make a mixture of 17 kg worth Rs.70 per kg. How many kilograms of each are taken ?

Options

A. 8 kg, 9 kg
B. 8 1/2 kg of each
C. 7 kg, 10 kg
D. None of these

Answer

To solve the problem of mixing currants at different prices to achieve a specific mixture price, we will use the method of alligation.

### Step-by-Step Solution:

1. **Identify the Prices and Mixture**:
- Price of first type of currants (P1) = Rs. 50 per kg
- Price of second type of currants (P2) = Rs. 90 per kg
- Mean price of the mixture (Pm) = Rs. 70 per kg
- Total weight of the mixture = 17 kg

2. **Set Up the Alligation**:
- We will apply the alligation formula to find the ratio in which the two types of currants are mixed.
- Calculate the differences:
- Difference between P2 and Pm: \( P2 - Pm = 90 - 70 = 20 \)
- Difference between Pm and P1: \( Pm - P1 = 70 - 50 = 20 \)

3. **Determine the Ratio**:
- The ratio of the quantities of the two types of currants is given by the differences calculated:
- Ratio = Difference from P2 : Difference from P1 = 20 : 20 = 1 : 1

4. **Calculate the Quantities**:
- Since the ratio is 1:1, it means that the quantities of both types of currants are equal.
- Let the quantity of each type of currant be \( x \) kg.
- Therefore, \( x + x = 17 \) kg
- This simplifies to \( 2x = 17 \)
- Solving for \( x \):
\[ x = \frac{17}{2} = 8.5 \text{ kg} \]

5. **Conclusion**:
- The quantity of currants at Rs. 50 per kg is 8.5 kg.
- The quantity of currants at Rs. 90 per kg is also 8.5 kg.

### Final Answer:
- Currants at Rs. 50 per kg: 8.5 kg
- Currants at Rs. 90 per kg: 8.5 kg