Practice Questions
Concept Explanation
To compare ratios, convert them to the same form — usually simplest form or decimal value of the first term divided by the second.
Compare 3 : 5 and 4 : 7: 3/5 = 0.6 and 4/7 ≈ 0.57, so 3 : 5 is larger.
For sharing problems, the ratio with the larger first term (for same second term) gives the larger first share.
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Q1 EasyArrange the ratios 3 : 4, 5 : 6 and 7 : 8 in ascending order of magnitude.Explanation3/4 = 0.75 < 5/6 ≈ 0.833 < 7/8 = 0.875.
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Q2 EasyWhich ratio is greater: 3 : 5 or 4 : 7?Explanation3/5 = 0.6 > 4/7 ≈ 0.571.
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Q3 EasyCompare 5 : 6 and 7 : 8. Which is greater?Explanation5/6 ≈ 0.833 and 7/8 = 0.875, so 7 : 8 is greater.
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Q4 EasyWhich ratio exceeds 1 : 1?Explanation7 : 6 is greater than 1 : 1.
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Q5 EasyCompare 9 : 12 and 12 : 16. They are:ExplanationBoth simplify to 3 : 4.
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Q6 MediumWhich of the following ratios is greatest?Explanation7/15 ≈ 0.467; 15/23 ≈ 0.652; 17/25 = 0.68; 21/29 ≈ 0.724. So 21 : 29 is greatest.
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Q7 MediumIf a/3 = b/4 = c/7, then (a + b + c)/c is equal to:Explanationa = 3k, b = 4k, c = 7k. Then (a+b+c)/c = 14k/7k = 2.
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Q8 MediumThe ratio of two numbers is 3 : 4 and their LCM is 180. The numbers are:ExplanationNumbers = 3k and 4k; LCM = 12k = 180 → k = 15. Numbers are 45 and 60.
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Q9 MediumIf 2A = 3B and 4B = 5C, then A : C is:ExplanationA/B = 3/2 and B/C = 5/4 → A/C = (3/2)×(5/4) = 15/8.
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Q10 MediumWhich of the following is the largest ratio?Explanation5/8 = 0.625 is the largest among the given options.
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Q11 MediumWhich ratio is the smallest?Explanation3/8 = 0.375 is the smallest.
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Q12 MediumWhich ratio is closest to 1 : 1?Explanation11/12 ≈ 0.917 is closest to 1.
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Q13 HardIf A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, then A : D is equal to:ExplanationA:B:C:D = 16:24:30:35 → A:D = 16:35.
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Q14 HardIf 2 : x > 3 : 5, then x is:Explanation2/x > 3/5 → 10 > 3x → x < 10/3.
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DS1 Easy
In a campus comparison drill, is ratio A greater than ratio B?
Statement IRatio A is 5 : 8.
Statement IIRatio B is 3 : 5.
Explanation5/8 = 0.625 and 3/5 = 0.6. Both statements are needed to compare. -
DS2 Easy
Is the ratio greater than 1 : 2?
Statement IThe ratio is 3 : 8.
Statement IIThe ratio simplifies to 3 : 8.
ExplanationEach alone shows 3/8 < 1/2, so the answer is no.
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DS3 Medium
Which of the two ratios is larger?
Statement IThe first ratio is 7 : 9.
Statement IIThe second ratio is 4 : 5.
Explanation7/9 ≈ 0.778 and 4/5 = 0.8, so the second is larger. Both needed. -
DS4 Medium
Are the two ratios equal?
Statement IThe first ratio simplifies to 2 : 3.
Statement IIThe second ratio is 10 : 15.
ExplanationEach alone identifies the ratio 2 : 3.