Ratio & Proportion in QAFB — Exam Shortcuts That Work

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Ratio and proportion is one of the most accessible topics in ICAP QAFB — and also one of the easiest to lose marks on due to careless errors rather than conceptual gaps. The right approach, with a few reliable shortcuts, makes these questions fast and accurate.

Understanding Ratios

A ratio compares two or more quantities of the same kind. It shows how much of one quantity exists relative to another.

Notation: a : b or a/b

Ratios can be simplified by dividing all parts by their highest common factor (HCF). For example, 24:36 simplifies to 2:3 (dividing both by 12).

Always simplify ratios to their lowest terms unless the question asks for a specific format. ICAP MCQs often present answer options in simplified form.

Dividing a Quantity in a Given Ratio

This is the most tested ratio application in ICAP QAFB. The method:

1. Add all parts of the ratio to get the total parts
2. Divide the total quantity by total parts to get the value of one part
3. Multiply each ratio component by the value of one part

Example

Divide Rs. 84,000 between Ali, Sara, and Ahmed in the ratio 3:4:5.

Total parts = 3 + 4 + 5 = 12

Value of 1 part = 84,000 ÷ 12 = Rs. 7,000

Ali = 3 × 7,000 = Rs. 21,000

Sara = 4 × 7,000 = Rs. 28,000

Ahmed= 5 × 7,000 = Rs. 35,000

Check: 21,000 + 28,000 + 35,000 = Rs. 84,000 ✓

Direct and Inverse Proportion

Direct Proportion

Two quantities are in direct proportion when they increase or decrease together at the same rate.

If y ∝ x then y = kx (where k is the constant of proportionality)

Example

If 8 workers produce 240 units per day, how many units will 5 workers produce?

Units per worker = 240 ÷ 8 = 30

5 workers × 30 = 150 units

Inverse Proportion

Two quantities are in inverse proportion when one increases as the other decreases.

If y ∝ 1/x then y = k/x or x₁y₁ = x₂y₂

Example

5 workers complete a job in 12 days. How many days will 3 workers take?

5 × 12 = 3 × d

d = 60 ÷ 3 = 20 days

Percentage and Ratio Conversions

ICAP QAFB frequently requires converting between ratios and percentages — a common point of error.

Ratio to percentage: Divide part by total, multiply by 100

Percentage to ratio: Express each percentage as a fraction, simplify to ratio form

Example

Ali owns 45% of a business, Sara 30%, and Ahmed 25%. Express ownership as a ratio.

45 : 30 : 25 → divide by 5 → 9 : 6 : 5

Common Exam Shortcuts

• For 'divide in ratio' questions — total parts first, always verify your answer sums to the original
• For inverse proportion — use the product rule: x₁y₁ = x₂y₂
• For percentage change questions — remember: % change = (New − Old) ÷ Old × 100
• Mark up vs margin — mark up is on cost, margin is on selling price (a classic ICAP trap)

Mark-up vs margin ICAP trap: If profit is 25% mark-up on cost of Rs. 80,000 → Profit = 25% × 80,000 = Rs. 20,000. If profit is 25% margin on selling price → Selling Price = Cost ÷ 0.75 = Rs. 106,667. These are very different answers.

Practice Ratio & Proportion on Preptio

Ratio, proportion, and percentage questions form a consistent block of ICAP QAFB marks. Preptio's QAFB question bank covers all variation types with step-by-step solutions so you can see exactly where your calculation approach diverged from the correct method.

Practice QAFB Ratio & Proportion on Preptio → preptio.com

Disclaimer: Preptio is a practice supplement — not a replacement for textbook study. Always cover your ICAP-recommended material alongside platform practice.