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15 Ratio & Proportion Questions and Answers
15 solved Ratio & Proportion questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.
Ratio and Proportion form the backbone of many quantitative problems in aptitude tests. A ratio compares two or more quantities of the same kind, while proportion establishes that two ratios are equal. Key concepts include direct proportion (as one increases, the other increases), inverse proportion (as one increases, the other decreases), and compound ratios. Common exam questions involve dividing amounts in a given ratio, finding unknown quantities from ratio relationships, and solving age-based or mixture-based ratio problems. The technique of introducing a common multiplier (x) is the most reliable approach. Below are solved questions covering all major ratio and proportion patterns.
If A:B = 3:8 and A = 42, what is B?
Simplify the ratio 21:13.
If A:B = 4:8 and A = 40, what is B?
Simplify the ratio 18:15.
If A:B = 7:3 and A = 84, what is B?
Simplify the ratio 23:8.
If A:B = 6:8 and A = 78, what is B?
Simplify the ratio 27:6.
Two numbers are in the ratio 6:3. If their sum is 117, find the first number.
If A:B = 9:9 and A = 126, what is B?
Two numbers are in the ratio 6:9. If their sum is 285, find the first number.
If A:B = 3:6 and A = 27, what is B?
Two numbers are in the ratio 3:2. If their sum is 100, find the first number.
If A:B = 9:5 and A = 54, what is B?
Simplify the ratio 28:17.
Key Takeaways
- Always introduce a common multiplier (x) when working with ratio problems.
- Sum of ratio parts × x gives the total; difference of ratio parts × x gives the difference.
- For compound ratios a:b and b:c: cross-multiply to get a:c.
- Units must match when comparing through ratios.
Frequently Asked Questions
How do I solve ratio problems?
Let the quantities be expressed as multiples of a common variable. For ratio a:b, let the values = a×x and b×x. Use the given total, sum, or difference to find x, then multiply to get actual values.
What is the difference between ratio and proportion?
A ratio compares two quantities (e.g., a:b). A proportion states that two ratios are equal (e.g., a:b :: c:d, meaning a/b = c/d). In a proportion, cross-multiplying gives ad = bc.
How do I divide a number in a given ratio?
Sum the ratio terms. Each share = Total × (ratio term ÷ sum of ratios). For ratio 2:3:5 with total 100, shares are 20, 30, and 50.
More Ratio & Proportion Practice Resources
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