Ratio and Proportion Tricks: Partnership, Mixture and Alligation Questions for SSC CGL, CHSL

Ratio and proportion is used in almost every chapter of SSC maths: partnership, mixture and alligation, ages, profit and loss, time and work. A student who is good in ratio can solve many other chapters quickly. These ratio and proportion tricks for SSC explain the types of proportion, how to divide a number in a ratio, and how to solve partnership, mixture and alligation questions.

Ratio and Proportion Basics

Combining Two Ratios

If A : B = 2 : 3 and B : C = 4 : 5, make B the same: A : B = 8 : 12 and B : C = 12 : 15. So A : B : C = 8 : 12 : 15.

Alligation (Mixing Two Items of Different Price)

Quantity of cheaper : Quantity of dearer = (d − m) : (m − c), where c = price of the cheaper, d = price of the dearer and m = price of the mixture.

Partnership

• Profit is divided in the ratio of (capital × time) of each partner.
• If the time is equal, the profit ratio is the ratio of the capitals.
• If the capital is equal, the profit ratio is the ratio of the times.

Solved Examples

Example 1. Divide 1,200 rupees in the ratio 3 : 5.
First = 3/8 × 1200 = 450 and second = 5/8 × 1200 = 750.

Example 2. Find the fourth proportional of 3, 6 and 5.
(6 × 5)/3 = 10.

Example 3. In what ratio must rice at 30 rupees a kg be mixed with rice at 50 rupees a kg to get a mixture of 35 rupees a kg?
(50 − 35) : (35 − 30) = 15 : 5 = 3 : 1.

Example 4 (partnership). A invests 5,000 rupees for 12 months and B invests 6,000 rupees for 6 months. Find the ratio of their profits.
60,000 : 36,000 = 5 : 3.

Example 5 (mixture). A mixture of 40 litres has milk and water in the ratio 3 : 2. How much milk is there? How much water must be added to make the ratio 1 : 1?
Milk = 3/5 × 40 = 24 L, water = 16 L. For the ratio 1 : 1, the water must be 24 L, so add 8 L.

Example 6 (ages). The ages of A and B are in the ratio 3 : 5, and their sum is 40 years. Find their ages.
A = 3/8 × 40 = 15 and B = 5/8 × 40 = 25 years.

Example 7. A number is divided in the ratio 2 : 3 : 5, and the smallest part is 20. Find the number.
One unit = 10, so the number = 10 × 10 = 100.

Tips

• Convert a ratio to units (1 unit, 2 units) and find the value of one unit first.
• Make the common term equal before you combine two ratios.
• In alligation, the mean price must lie between the two prices.
• In partnership, always multiply the capital by the time.

Quick Tips

• Find the value of one unit first.
• Make the common term equal to combine two ratios.
• Use the alligation cross for mixtures of two prices.
• In partnership, multiply capital by time.

Quick Revision Points

• Proportion: product of extremes = product of means.
• Mean proportion = √(ab) and third proportion = b²/a.
• Alligation: cheaper : dearer = (d − m) : (m − c).
• Partnership profit ratio = capital × time.
• Make the common term equal to combine ratios.

Practice Questions With Answers

1. Divide 900 rupees in the ratio 2 : 3.
   Answer: 360 and 540 rupees
2. Find the mean proportion of 4 and 25.
   Answer: 10
3. Find the third proportion of 9 and 12.
   Answer: 16
4. In what ratio must rice at 30 and rice at 50 rupees be mixed to get a mixture of 35 rupees?
   Answer: 3 : 1
5. The ratio of the ages of A and B is 3 : 5 and their sum is 40 years. Find A’s age.
   Answer: 15 years
6. If A : B = 2 : 3 and B : C = 4 : 5, find A : C.
   Answer: 8 : 15
7. A invests 4,000 rupees for 12 months and B invests 6,000 rupees for 8 months. The profit is 3,000 rupees. Find A’s share.
   Answer: 1,500 rupees
8. A mixture of 40 L has milk and water in the ratio 3 : 2. Find the milk.
   Answer: 24 L
9. A number is divided in the ratio 2 : 3 : 5 and the smallest part is 20. Find the number.
   Answer: 100
10. Find the fourth proportional of 3, 6 and 5.
    Answer: 10

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Mathematics notes page, read the previous topic Average Tricks and the next topic Time and Work Tricks. Formulas are in the Formula Guide and more practice is in the Quantitative Aptitude notes.

Frequently Asked Questions

What is a ratio?

A ratio compares two quantities of the same kind, written as a : b.

What is a proportion?

A proportion is an equality of two ratios, a : b = c : d.

What is the mean proportion of two numbers?

It is the square root of their product.

What is the third proportion of a and b?

It is b squared divided by a.

What is alligation?

It is a method to find the ratio in which two items of different prices are mixed.

How is the profit divided in a partnership?

In the ratio of capital multiplied by time.

How do I combine two ratios A:B and B:C?

Make B equal in both ratios and then write A : B : C.

What is a unit method in ratio?

It means to take one part of the ratio as 1 unit and find its value.

Is ratio asked in SSC exams?

Yes. Ratio and proportion questions are asked in every SSC maths paper.

What are common mistakes?

Not making the common term equal and adding the ratio parts wrongly.

How much time should I take?

About 40 seconds.

What is the compounded ratio?

It is the product of the two ratios, ac : bd.