Ratio, Proportion and Alligation: The Shortcuts That Work

Ratio questions are among the most common in quantitative aptitude, and they're usually quick once you know the standard approaches.

Basic ratio

A ratio compares two quantities. 3 : 5 means for every 3 of one there are 5 of the other.

Splitting an amount in a ratio

To divide 900 in the ratio 2 : 3 : 4:

1. Add the parts: 2 + 3 + 4 = 9.
2. One part = 900 ÷ 9 = 100.
3. The shares are 200, 300 and 400.

Proportion

Two ratios are in proportion if a : b = c : d, meaning a × d = b × c.

Example: If 6 pens cost 45, what do 10 pens cost? 6 : 45 = 10 : x, so x = 45 × 10 ÷ 6 = 75.

Age problems

Example: The ages of two people are in the ratio 3 : 5, and their sum is 40. Their ages are:

• One part = 40 ÷ 8 = 5.
• Ages = 15 and 25.

To find ages after some years, add the years to each actual age, not to the ratio parts.

Mixtures and alligation

Alligation finds the ratio in which two items must be mixed to get a desired average.

Example: Rice at 40 per kg and 50 per kg is mixed to sell at 44 per kg. In what ratio?

	Price
Cheaper	40
Mean	44
Dearer	50

Differences: 50 − 44 = 6 and 44 − 40 = 4, so the cheaper and dearer are mixed in the ratio 6 : 4 = 3 : 2.

Check: (40 × 3 + 50 × 2) ÷ 5 = 220 ÷ 5 = 44.

Weighted average

If 3 kg costs 40 per kg and 2 kg costs 50 per kg, the average price is (120 + 100) ÷ 5 = 44.

Tips

1. Convert to a common unit before forming a ratio.
2. Keep the order of the ratio consistent.
3. Check your answer by substituting back.

Practice

Short daily sets on ratio and mixtures build the speed exams demand.

Practise with Online Exam Question & Answer →