Find the Compound Ratio of a:b and c:d

Question

Find the Compound Ratio of a:b and c:d

1. A. ac:bd (Correct answer)
2. B. ab:cd
3. C. ad:bc
4. D. ab:bcd

Correct Answer

Option A — A

Detailed Solution & Explanation

The correct answer is Option A.

Key Points

• The compound ratio of two ratios is obtained by multiplying the antecedents together and the consequents together.
• Compound ratio of a : b and c : d = (a × c) : (b × d) = ac : bd.

Exam Tip

• compound ratio multiplies (a:b compounded with c:d = ac:bd); the duplicate ratio of a:b is a²:b², and the sub-duplicate is √a:√b. Keep these operations distinct.

Additional Information

• The compound ratio of a : b and c : d is ac : bd — multiply antecedents together and consequents together.
• Related operations: duplicate ratio a² : b², sub-duplicate √a : √b, triplicate a³ : b³, and the inverse ratio b : a.
• Compound ratios underpin work-and-time and speed problems, where several ratios combine multiplicatively.