Compound Ratio: Formula, Rules and Solved Questions

Compound Ratio combines two or more ratios by multiplying their corresponding terms. For ratios a:b and c:d, the compound ratio is ac:bd. This page explains the compound ratio formula, ratio multiplication, simplification rules and direct methods for solving numerical questions involving two or more given ratios.

On this page

What Is Compound Ratio?

The compound ratio of a:b and c:d is the ratio obtained by multiplying the first terms together and the second terms together. Thus, the compound ratio is ac:bd.

For example, the compound ratio of 2:3 and 4:5 is (2 × 4):(3 × 5) = 8:15. The resulting ratio should be reduced to its simplest form whenever the two product terms have a common factor.

Compound Ratio Formula & Tricks

Important Formulas

Compound ratio of two ratios
Compound ratio of a:b and c:d = (a × c):(b × d) = ac:bd

Multiply the corresponding first terms and corresponding second terms.

Compound ratio of multiple ratios
a₁:b₁, a₂:b₂, ..., aₙ:bₙ → (a₁a₂...aₙ):(b₁b₂...bₙ)

Multiply all the first terms to obtain the first part and all the second terms to obtain the second part.

Simplification
If the compound ratio is x:y, simplest form = (x ÷ g):(y ÷ g), where g = HCF(x,y)

Divide both terms by their highest common factor.

Quick Tricks

Cancel common factors before multiplying

Common factors can be cancelled between the factors in the first product and the factors in the second product before carrying out multiplication. This reduces large calculations.

Example: For 6:35 and 14:15, the compound ratio is 6 × 14 : 35 × 15. Cancelling 6 with 15 and 14 with 35 gives 4:25 directly.
Keep corresponding positions together

Multiply first terms with first terms and second terms with second terms. Do not cross-multiply the terms while forming a compound ratio.

Example: The compound ratio of 3:4 and 5:6 is 15:24, which simplifies to 5:8. The cross-products 3 × 6 and 4 × 5 do not form the compound ratio.

Compound Ratio Concepts

Compound Ratio of Three or More Ratios

For three or more ratios, multiply all first terms together and all second terms together.

If the ratios are a:b, c:d and e:f, their compound ratio is (a × c × e):(b × d × f). The same method extends to any number of ratios.

Example: For 2:3, 4:5 and 6:7, the compound ratio is (2 × 4 × 6):(3 × 5 × 7) = 48:105 = 16:35.

Simplifying a Compound Ratio

After multiplication, divide both terms of the resulting ratio by their HCF.

For example, 4:6 and 9:10 give 36:60. Since HCF(36, 60) = 12, the simplest compound ratio is 3:5. Dividing both terms by the same positive number preserves the ratio.

Example: Compound ratio = (4 × 9):(6 × 10) = 36:60 = 3:5.

Order of Terms in Ratio Multiplication

The first term of every ratio must be multiplied with the first term of every other ratio, and the second terms must be multiplied together.

For ratios 3:4 and 5:6, the correct compound ratio is 3 × 5:4 × 6 = 15:24. Cross-products are not used because they change the required correspondence between the two parts.

Example: For 7:9 and 2:5, compound ratio = (7 × 2):(9 × 5) = 14:45.

Finding an Unknown Term

If one term of a compound ratio is unknown, form the product ratio first and equate it to the given ratio.

For example, if the compound ratio of x:3 and 4:5 is 8:15, then 4x:15 = 8:15. Therefore, 4x = 8 and x = 2.

Example: The compound ratio of 2:3 and 4:5 is 8:15, so x = 2 when the first ratio is x:3 and the compound ratio is 8:15.

Compound Ratio Video Lessons

Watch short topic-wise lessons for quick revision.

4 Lessons
Lesson 1 of 4 Quick Revision

Duplicate, Triplicate and Sub-Duplicate Ratios

Learn the definitions and application of duplicate, triplicate, and sub-duplicate ratios, with clear methods for understanding how these special ratios are formed and used.

Continue with more lessons and practice in PrepShots.Watch More in App - Start ₹1 Trial →
More Compound Ratio Lessons Scroll to explore →

Practice Compound Ratio Questions

Practise published questions related to this topic.

1The largest four-digit number which when divided by 10, 11 and 8 leaves remainder 7 in each case is:→ 2During a sale 50% of the goods are sold at 40% profit, 40% of the remaining goods are sold at 13% profit and the still remaining goods are sold at a loss of 32%. If there is an overall profit of x%, then what is the value of x?→ 3Which of the following will have marked price Rs. 4000?→ 4If 6x - 6x-1 = 180, then the value of (2x-1)/(2x+3) is:→ 5If the ratio of two numbers is 6 : 7, and their HCF is 9, then their LCM is:→ 6If an item marked at ₹1,675 is sold for ₹1,273, then what is the discount percentage?→ 7The marked price of a painting was ₹7,500, but the shopkeeper offered a double discount in a successive manner of 14% and 28%. Ultimately for how much did he sell the item?→ 8If X = √169 × √121+√64, then what is the value of 2x?→ 9√(0.16/0.0004) × √(0.25/0.49) = ?→ 10If x+6 is the HCF of x² + 10x + 24 and x² + kx + 12 , then the value of k is:→

Compound Ratio Quick Quiz

Attempt 5 questions and check your score instantly.

Quick Revision Notes

Compound Ratio Revision Points

Use these rules to revise the calculation and simplification of compound ratios.

  • For a:b and c:d, compound ratio = ac:bd.
  • For several ratios, multiply all first terms and all second terms separately.
  • Reduce the final ratio by dividing both terms by their HCF.
  • Common factors may be cancelled before multiplication.
  • Do not cross-multiply corresponding terms while forming a compound ratio.
  • The compound ratio of 2:3, 4:5 and 6:7 is 48:105 = 16:35.

Compound Ratio FAQs

What is the compound ratio of 3:4 and 5:8?

Multiply corresponding terms: (3 × 5):(4 × 8) = 15:32. Therefore, the compound ratio is 15:32.

What is the compound ratio of 2:3, 4:5 and 6:7?

It is (2 × 4 × 6):(3 × 5 × 7) = 48:105 = 16:35.

Can a compound ratio be simplified before multiplication?

Yes. Common factors can be cancelled between the factors in the two products before multiplication, provided the same factor is cancelled from both sides.

What is the difference between compound ratio and cross multiplication?

Compound ratio multiplies first terms together and second terms together. Cross multiplication forms products such as a × d and b × c, so it is not the method for finding a compound ratio.

If the compound ratio of x:3 and 4:5 is 8:15, what is x?

The compound ratio is 4x:15. Equating 4x:15 to 8:15 gives 4x = 8, so x = 2.

Continue learning Compound Ratio on PrepShots

Continue on PrepShots