In what ratio must wheat at Rs. 1.60 per kg be mixed with wheat at Rs. 1.45 per kg so that the mixture is worth Rs. 1.54 per kg (no wastage)?

Introduction / Context:
Alligation is the quickest way to find the mixing ratio for a target mean price between two known prices. The quantities are inversely proportional to the differences from the mean.

Given Data / Assumptions:

• Dearer wheat: Rs. 1.60/kg.
• Cheaper wheat: Rs. 1.45/kg.
• Mixture price: Rs. 1.54/kg.

Concept / Approach:
For prices P1 (dearer) and P2 (cheaper) yielding mean M, the required ratio P1 : P2 = (M − P2) : (P1 − M).

Step-by-Step Solution:
Differences: M − P2 = 1.54 − 1.45 = 0.09P1 − M = 1.60 − 1.54 = 0.06Hence 1.60 : 1.45 quantities = 0.09 : 0.06 = 3 : 2

Verification / Alternative check:
Weighted average with 3 kg of 1.60 and 2 kg of 1.45: price = (3*1.60 + 2*1.45)/5 = (4.80 + 2.90)/5 = 7.70/5 = 1.54.

Why Other Options Are Wrong:
2 : 3 or 4 : 3 give means other than 1.54; only 3 : 2 balances the differences correctly.

Common Pitfalls:
Using direct differences instead of inverse differences, which reverses the intended ratio.

Final Answer:
3 : 2