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In what ratio, rice at ₹28.80 per kg and rice at ₹ 22.80 per kg be mixed to get a mixture worth ₹ 25.20 per kg ?
Question

In what ratio, rice at ₹28.80 per kg and rice at ₹ 22.80 per kg be mixed to get a mixture worth ₹ 25.20 per kg ?

A.

1:3

B.

2:3

C.

3:4

D.

5:3

Correct option is B

Given:
Price of first type of rice = ₹ 28.80 per kg
Price of second type of rice = ₹ 22.80 per kg
Price of the mixed rice = ₹ 25.20 per kg
Formula Used:
Rule of Alligation:
​Quantity of CheaperQuantity of Dearer=Price of Dearer−Mean PriceMean Price−Price of Cheaper\frac{Quantity\ of\ Cheaper}{Quantity\ of\ Dearer} = \frac{Price\ of\ Dearer - Mean\ Price}{Mean\ Price - Price\ of\ Cheaper}​​
Solution:
Apply the rule of alligation:
Cost of cheaper rice (C) = 22.80
Cost of dearer rice (D) = 28.80
Mean price (M) = 25.20
Find the differences:
D - M = 28.80 - 25.20 = 3.60
M - C = 25.20 - 22.80 = 2.40
The ratio of their quantities is:
Ratio = 3.602.40 \frac{3.60}{2.40}​​=32= \frac{3}{2}​​
However, the question asks for the ratio of dearer to cheaper rice (since 28.80 is mentioned first):
Required Ratio =  (M−C):(D−M)=2.40:3.60=2:3(M - C) : (D - M) = 2.40 : 3.60 = 2 : 3​​
Final Answer
So the correct answer is (b)

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