Patwari Exam · Reasoning
Ratio, Proportion & Average
This note explains ratio, proportion, partnership, weighted average, and average-change questions with examples.
- Reasoning & Numerical Ability
- 5 min read
Verified 6 October 2026
Key Formulas & Methods
- Ratio basics
- Ratio: a:b = a/b; if a:b = 2:3 and b:c = 4:5 then a:b:c = 8:12:15.
- Proportion rule
- Proportion: a:b::c:d ⟹ a×d = b×c (product of extremes = product of means).
- Partnership profit-sharing
- Partnership: profit is shared in the ratio of investment × time.
- Average formula
- Average = total sum / number of items.
- Weighted average
- Weighted average: (a₁w₁ + a₂w₂)/(w₁+w₂) where w = weight.
- Average change
- If the average increases/decreases by n: total change = n × number of members.
- Worked example
- Exam example: the average of 5 numbers is 20; after removing one, the average is 18 → removed number = 5×20 − 4×18 = 100−72 = 28.
Frequently Asked Questions
What is the rule for proportion?+
If a:b::c:d, then the product of extremes equals the product of means, i.e. a×d = b×c.
How is the average calculated?+
Average = total sum / number of items, and weighted average is found using (a₁w₁ + a₂w₂)/(w₁+w₂), where w is the weight.
How is profit shared in a partnership?+
In a partnership, profit is shared in the ratio of investment × time.