Question

Two distinct grades of rice, one priced at ₹80 per kilogram and the other at ₹120 per kilogram, are amalgamated in an undisclosed proportion. The resultant blend is retailed at ₹132 per kilogram, securing a profit margin of 20% on the overall cost price. Determine the precise ratio in which the two rice varieties were intermingled.

• A. 1 : 3
• B. 2 : 1
• C. 3 : 2
• D. 3 : 1

Answer 1

Answer:

A. 1 : 3

Selling price = ₹132/kg with 20% profit.

Step 1: Find the cost price of the mixture

$CP=\frac{132\times100}{120}$=₹110/kg

So, the mixture must have an average cost of ₹110/kg.

Step 2: Use the allegation method

Rice	Price	Difference from ₹110
₹80/kg	80	(110-80=30)
₹120/kg	120	(120-110=10)

Therefore, the ratio is:

$\text{Rs.80 rice : Rs.120 rice}=10:30$
$\boxed{1:3}$

Answer: 1 : 3

So, 1 kg of ₹80 rice is mixed with 3 kg of ₹120 rice.