Quantity Comparison (I vs II) — IBPS PO
Quantity comparison gives you two quantities — Quantity I and Quantity II — each defined by a small problem, and asks for the relation between them. It's a newer Mains format that packages ordinary arithmetic (percentage, ratio, ages, simple equations) into a fixed comparison key. The efficient approach is rarely to compute both quantities fully — often you can estimate, cancel a common factor, or reason about magnitude to decide the relation faster. At 0–5 Mains marks, treating it as "compare, don't fully solve" is the time-saver.
1. What IBPS actually asks
Two quantities and the fixed key:
- Quantity I > Quantity II
- Quantity I < Quantity II
- Quantity I ≥ Quantity II
- Quantity I ≤ Quantity II
- Quantity I = Quantity II or relation cannot be established
Each quantity is a mini arithmetic problem — a percentage, an average, roots of a quadratic, a probability, a speed. Read the exact option order printed with the set.
2. The method: compute (or estimate) each, then compare
- Solve Quantity I to a value (or a range/roots).
- Solve Quantity II likewise.
- Compare and map to the key — using ≥/≤ if equality is possible, or "cannot be established" if the values interleave (as with quadratic roots).
But before grinding both out fully, look for a shortcut.
3. Estimate and cancel — the speed move
You often don't need exact values:
- Magnitude estimate: if Quantity I is clearly "around 200" and Quantity II is "around 350", you're done — no exact figures needed.
- Cancel a common structure: if both are
k × something, compare thesomething. - Compare like-for-like: two percentages of the same base, or two fractions by cross-multiplication (
a/bvsc/d⇒advsbc).
Ask "do I actually need the exact values, or just which is bigger?" Usually the latter — and estimation gets you there in half the time.
4. The quadratic / range case (cannot be established)
When a quantity comes from a quadratic (two roots) or a range, the comparison can be ambiguous:
- Quantity I = roots {2, 3}, Quantity II = 2.5 ⇒ I could be 2 (< II) or 3 (> II) ⇒ relation cannot be established.
- Only when every value of one quantity is consistently ≥ / ≤ the other is a definite relation possible (this mirrors the Quadratic Equations chapter).
Don't force a > or < when the quantity is a set of values that straddle the other.
5. The equality subtlety
- Use ≥ / ≤ when the quantities can be equal in some case but one is otherwise larger.
- Use = only when they are always exactly equal.
- If a clean single comparison isn't possible and it's not an either–case, it's "cannot be established".
Solved examples
Q1. Quantity I: 25% of 240. Quantity II: ⅓ of 180.
Show explanation
Solution. I = 60; II = 60 ⇒ Quantity I = Quantity II (option 5).
Q2. Quantity I: the average of 12, 18, 30. Quantity II: 25% of 80.
Show explanation
Solution. I = 60/3 = 20; II = 20 ⇒ I = II.
Q3 (estimate). Quantity I: 18% of 449. Quantity II: 21% of 351.
Show explanation
Solution. I ≈ 0.18×450 ≈ 81; II ≈ 0.21×350 ≈ 73.5 ⇒ Quantity I > Quantity II. (No exact computation needed.)
Q4 (quadratic). Quantity I: roots of x² − 5x + 6 = 0. Quantity II: 2.5.
Show explanation
Solution. Roots x = 2, 3. Since 2 < 2.5 < 3, the roots straddle II ⇒ relation cannot be established.
7. The protocol
- Read the exact option key.
- Before computing, look for an estimate or cancellation — do you need exact values or just the bigger one?
- Solve each quantity (or estimate) to a value/range.
- Compare and map to the key; use ≥/≤ for possible equality.
- If one quantity is a set of values that straddles the other (quadratic/range), the answer is cannot be established.
