Practice Questions
Concept Explanation
Two quantities are in direct proportion if they increase or decrease together. Product of extremes = product of means.
If x ∝ y, then x/y = constant, or x₁/y₁ = x₂/y₂.
Examples: cost vs number of items, distance vs time at constant speed.
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Q1 EasyIf 15% of x = 20% of y, then x : y is:Explanation0.15x = 0.20y → x/y = 4/3.
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Q2 EasyIf 4 : 5 = x : 20, then x equals:Explanation4 × 20 = 5x → x = 16.
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Q3 EasyIf 5 books cost Rs. 250, what is the cost of 8 books?ExplanationCost per book = Rs. 50. Cost of 8 books = Rs. 400.
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Q4 EasyCost varies directly with quantity. If 4 kg costs Rs. 120, what is the cost of 10 kg?ExplanationRate = Rs. 30 per kg. Cost of 10 kg = Rs. 300.
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Q5 EasyIf y varies directly with x and y = 24 when x = 6, what is y when x = 9?Explanationy/x = 4. When x = 9, y = 36.
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Q6 EasyDistance travelled varies directly with time at constant speed. In 4 hours a car covers 240 km. How far does it travel in 7 hours?ExplanationSpeed = 60 km/h. Distance in 7 hours = 420 km.
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Q7 EasyIf a/b = 3/4 and b = 28, what is the value of a?Explanationa = (3/4) × 28 = 21.
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Q8 MediumIf x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is:ExplanationPut x = 5k, y = 2k. Then (40k+18k):(40k+4k) = 58k:44k = 29:22.
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Q9 MediumIf a/b = 2/3 and b/c = 4/5, then a : b : c is:Explanationa:b = 2:3 and b:c = 4:5 → a:b:c = 8:12:15.
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Q10 MediumIf 2, 5, x, 20 are in proportion, then x is:Explanation2/5 = x/20 → 2 × 20 = 5x → x = 8.
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Q11 MediumOn a map, 2 cm represents 5 km. What actual distance is represented by 8 cm on the map?ExplanationActual distance = (8/2) × 5 = 20 km.
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Q12 MediumIf 7 : x = 21 : 30, then x equals:Explanation21x = 210 → x = 10.
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Q13 MediumPrinting cost is directly proportional to the number of pages. If 50 pages cost Rs. 75, what is the cost of 120 pages?ExplanationCost per page = Rs. 1.50. Cost of 120 pages = Rs. 180.
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Q14 HardWhat number must be added to each term of the ratio 7 : 13 so that the ratio becomes 2 : 3?Explanation(7+x)/(13+x) = 2/3 → 21 + 3x = 26 + 2x → x = 5.
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DS1 Easy
During a retail pricing drill, what is the cost of 10 identical items?
Statement I5 items cost Rs. 200.
Statement IICost varies directly with the quantity purchased.
ExplanationTogether: rate = Rs. 40 per item, so 10 items cost Rs. 400. -
DS2 Easy
What is the value of x in the proportion?
Statement I3 : 7 = x : 28.
Statement IIx is a positive integer.
ExplanationStatement I alone: x = 12.
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DS3 Medium
How far will the car travel in 5 hours?
Statement IIt travels 180 km in 3 hours at constant speed.
Statement IIDistance varies directly with time.
ExplanationSpeed = 60 km/h → distance in 5 hours = 300 km from Statement I alone. -
DS4 Medium
What is the value of y when x = 8?
Statement Iy varies directly with x.
Statement IIy = 15 when x = 5.
ExplanationTogether: y/x = 3, so when x = 8, y = 24.