Practice Questions
Concept Explanation
Two ratios are equivalent if they represent the same relationship — they simplify to the same lowest form, or one can be obtained by multiplying/dividing both terms of the other by the same non-zero number.
Example: 2 : 3 = 4 : 6 = 10 : 15.
Test for Equivalence
Cross-multiply: a : b = c : d if a × d = b × c.
Finding Missing Term
If 3 : 5 = x : 20, then 3 × 20 = 5x → x = 12.
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Q1 EasyWhich ratio is equivalent to 2 : 5?Explanation2 : 5 = 6 : 15 when both terms are multiplied by 3.
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Q2 EasyIf 5 : 8 = x : 24, then x is:Explanation5 × 24 = 8x → x = 15.
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Q3 EasyIf 2 : 3 = 8 : x, then x equals:Explanation2x = 24 → x = 12.
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Q4 EasyRatio 18 : 24 is equivalent to:ExplanationDivide both terms by 6: 3 : 4.
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Q5 MediumIf 0.75 : x :: 5 : 8, then x is equal to:Explanation0.75/x = 5/8 → 5x = 6 → x = 1.2.
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Q6 MediumIf a : b = 3 : 4 and b : c = 8 : 9, then a : c is:Explanationa : b : c = 6 : 8 : 9 → a : c = 6 : 9 = 2 : 3.
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Q7 MediumThe ratio of two numbers is 3 : 5 and their H.C.F. is 4. Their L.C.M. is:ExplanationNumbers = 12 and 20. LCM = 60.
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Q8 MediumIf 2A = 3B = 4C, then A : B : C is:ExplanationLet 2A = 3B = 4C = 12k. Then A = 6k, B = 4k, C = 3k → A:B:C = 6:4:3.
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Q9 MediumWhich is NOT equivalent to 4 : 7?Explanation20 : 30 = 2 : 3, which is not equal to 4 : 7.
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Q10 MediumExpress 0.75 : 1 in simplest integer ratio.Explanation0.75 : 1 = 3/4 : 1 = 3 : 4.
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Q11 MediumTwo ratios 8 : 12 and 14 : 21 are:ExplanationBoth simplify to 2 : 3, so they are equivalent.
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Q12 HardIf (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and a + b + c = 14, then the value of c is:Explanation2(a+b+c) = 6k+7k+8k = 21k = 28 → k = 4/3. Then c = (a+b+c) − (a+b) = 14 − 6k = 14 − 8 = 6.
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Q13 HardIf A : B = 1 : 3, B : C = 5 : 7 and C : D = 9 : 11, then A : D is equal to:ExplanationA:B:C:D = 1×5×9 : 3×5×9 : 3×7×9 : 3×7×11 = 45 : 135 : 189 : 231 → A:D = 45:231 = 15:77.
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Q14 HardWhich ratio equals 1/3 : 1/2?ExplanationMultiply both terms by 6: 2 : 3.
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DS1 Easy
In an aptitude screening, are the two ratios equivalent?
Statement IThe ratios are 6 : 10 and 9 : 15.
Statement IIBoth ratios simplify to 3 : 5.
ExplanationEach statement alone confirms that both ratios equal 3 : 5. -
DS2 Easy
During a campus drill, what is the missing term x?
Statement I3 : 5 = x : 40.
Statement IIx is an even number less than 30.
ExplanationStatement I alone: x = 24.
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DS3 Medium
A trainer asks for the simplest form of a ratio. What is the simplest form of the ratio?
Statement IThe ratio is 48 : 72.
Statement IIBoth terms are divisible by 24.
ExplanationStatement I alone gives 2 : 3. -
DS4 Medium
Is the given ratio equivalent to 4 : 7?
Statement IThe ratio is 20 : 35.
Statement IIThe ratio is 12 : 21.
ExplanationEach alone simplifies to 4 : 7.