How much rice of ₹4 per kg should be mixed with 15 kg of rice of ₹10 per kg to make a mixture worth ₹6.50 per kg?

Question

Accepted Answer

Let the quantity of rice costing ₹4 per kg be x kg.

Given:
- Quantity of rice costing ₹10 per kg = 15 kg
- Price of cheaper rice = ₹4 per kg
- Price of dearer rice = ₹10 per kg
- Price of mixture = ₹6.50 per kg

Using the allegation method:

Difference between price of dearer rice and mixture = 10 - 6.5 = 3.5
Difference between price of mixture and cheaper rice = 6.5 - 4 = 2.5

Ratio of quantities = 3.5 : 2.5 = 7 : 5

Since the quantity of dearer rice is 15 kg, quantity of cheaper rice = (5/7) * 15 = 75/7 = 10.71 kg approx.

But this contradicts the options given, so let's use the algebraic method:

Total cost of mixture = (15 * 10) + (x * 4)
Total quantity = 15 + x

Price of mixture = Total cost / Total quantity
6.5 = (150 + 4x) / (15 + x)

Multiply both sides by (15 + x):
6.5(15 + x) = 150 + 4x
97.5 + 6.5x = 150 + 4x
6.5x - 4x = 150 - 97.5
2.5x = 52.5
x = 52.5 / 2.5 = 21 kg

Therefore, 21 kg of rice costing ₹4 per kg should be mixed.

Answer

Answer

Answer