Quantity comparison (Q1 vs Q2) for IBPS PO

Quantity comparison gives you two quantities, each defined by a short problem. You work out both and say how they compare. It looks like a word-problem set, but it rewards a different habit: you only need enough precision to compare, not a polished answer.

Each quantity can come from any arithmetic topic: percentages, interest, profit, speed, work, probability, a quadratic equation. So a set of five can test five different chapters in five minutes. It appears in both the prelims (often alternating with quadratic equation sets) and the mains.

The answer options

Some papers keep "equal" and "cannot be established" as separate options, and some join them. Read the last option at the start of the set.

How it differs from quadratic equations

In a quadratic equations set, both quantities come from the same kind of equation. Here, each side is a different problem, and one side is often just a number. The comparison logic is identical: if either quantity has more than one possible value, compare every value against every value.

The method

1. Solve the easier quantity first. If Quantity II is simply "50", you know your target before starting Quantity I.
2. Solve only as far as needed. If Quantity I is clearly over 60 and Quantity II is 50, stop.
3. Convert to the same units. m/s against km/h, months against years, paise against rupees.
4. List every possible value. A quadratic gives two; x² = k gives two; √k gives one.
5. Compare every pair, then pick the option.

Eight worked examples

Example 1: Quantity I: 20% of 450. Quantity II: 25% of 360.

• I = 90. II = 90.
• Answer: I = II.

Example 2: Quantity I: SI on ₹5,000 at 10% a year for 2 years. Quantity II: CI on ₹5,000 at 10% a year for 2 years, compounded annually.

• I = 5,000 × 10 × 2 ÷ 100 = ₹1,000.
• II = 5,000 × 1.21 − 5,000 = ₹1,050.
• Answer: I < II. For 2 or more years at the same rate, CI always exceeds SI, so you could answer without calculating.

Example 3: Quantity I: x, where x² − 8x + 15 = 0. Quantity II: 4.

• x = 3 or 5. 3 < 4 but 5 > 4.
• Answer: relation cannot be established.

Example 4: Quantity I: speed in km/h of a 150 m train that crosses a pole in 10 seconds. Quantity II: 50.

• 150 ÷ 10 = 15 m/s. 15 × 18/5 = 54 km/h.
• Answer: I > II. Comparing 15 with 50 would have given the wrong answer.

Example 5: Quantity I: x, where x² − 7x + 12 = 0. Quantity II: y, where y² − 9y + 20 = 0.

• x = 3, 4. y = 4, 5.
• Every x is at most every y, and 4 = 4.
• Answer: I ≤ II.

Example 6: Quantity I: probability of a sum of 7 when two fair dice are thrown. Quantity II: probability of drawing a king from a well-shuffled pack of 52 cards.

• I: favourable pairs (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 of 36 = 1/6.
• II: 4/52 = 1/13.
• 1/6 > 1/13. Answer: I > II.

Example 7: Quantity I: M's present age, if the ages of M and N are in the ratio 3 : 4 and add up to 56. Quantity II: the present age of a person who was 20 four years ago.

• I: 56 × 3/7 = 24. II: 20 + 4 = 24.
• Answer: I = II.

Example 8: Quantity I: the number of ways to choose 2 people from 6. Quantity II: the number of ways to arrange 3 different books in a row.

• I: 6C2 = (6 × 5) ÷ 2 = 15. II: 3! = 6.
• Answer: I > II.

Common traps

• Stopping after one root. Two roots mean two comparisons.
• Treating √k as ±. The √ sign means the positive root only. x² = 81 gives ±9, but √81 is 9.
• Comparing different units. Always convert before comparing.
• Choosing "equal" too soon. If one pair is equal but another pair is not, the answer is ≥, ≤ or "cannot be established", not "equal".
• Over-calculating. If the two quantities are far apart, an estimate is enough.

Practice set

1. Quantity I: 3/8 of 640. Quantity II: 40% of 600.
2. Quantity I: the average of 12, 18 and 24. Quantity II: the median of 10, 17 and 30.
3. Quantity I: CI on ₹10,000 at 20% for 2 years, compounded annually. Quantity II: SI on ₹10,000 at 22% for 2 years.
4. Quantity I: y, where y² = 36. Quantity II: 5.
5. Quantity I: days taken by A and B together, if A alone takes 20 days and B alone 30 days. Quantity II: 10.
6. Quantity I: x, where x² = 81. Quantity II: y, where y = √81.
7. Quantity I: speed of a boat in still water (km/h) if it goes 36 km downstream in 3 hours and 36 km upstream in 4 hours. Quantity II: 10.
8. Quantity I: overall loss percentage when two items are each sold for ₹990, one at 10% profit and one at 10% loss. Quantity II: 1.

Answers:

1. I = II. Both are 240.
2. I > II. Average 54 ÷ 3 = 18; median 17.
3. I = II. CI = 10,000 × 1.44 − 10,000 = ₹4,400. SI = 10,000 × 22 × 2 ÷ 100 = ₹4,400.
4. Relation cannot be established. y = 6 or −6; 6 > 5 but −6 < 5.
5. I > II. 1/20 + 1/30 = 5/60 = 1/12, so 12 days.
6. I ≤ II. x = 9 or −9; y = 9.
7. I > II. Downstream 12 km/h, upstream 9 km/h. Boat = (12 + 9) ÷ 2 = 10.5.
8. I = II. Cost prices 900 and 1,100 total 2,000; selling prices total 1,980; loss 20 ÷ 2,000 = 1%.

What to do next

• Do one set of five a day for two weeks, each set in under five minutes.
• After each set, note which topic slowed you down, and revise that chapter: percentage, interest or averages and ages.
• Alternate with quadratic equation sets so the comparison logic stays automatic.