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In what ratio must rice at ₹ 60 per kg is mixed with rice at ₹ 90 per kg so that the mixture be worth ₹ 80 per kg?

Solution

✅ Correct Option: 4

Two types of rice need to be mixed:

  • Rice at ₹60 per kg
  • Rice at ₹90 per kg
  • Desired mixture price: ₹80 per kg

Using the Alligation Method:

Ratio = (Higher Price - Mean Price) : (Mean Price - Lower Price)

Where:

  • Higher Price = ₹90
  • Lower Price = ₹60
  • Mean Price = ₹80

Ratio = (90 - 80) : (80 - 60)

Ratio = 10 : 20

Ratio = 1 : 2


The rice at ₹60 per kg must be mixed with rice at ₹90 per kg in the ratio 1:2.

This means 1 kg of ₹60 rice is mixed with 2 kg of ₹90 rice.

Total Cost = (1 × 60) + (2 × 90) = 60 + 180 = ₹240

Total Quantity = 1 + 2 = 3 kg

Average price per kg = 2403=80\dfrac{240}{3} = 80 per kg

Therefore, the answer is 1:2.

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