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 Easy
If 5 books cost Rs. 250, cost of 8 books is:
ExplanationCost per book = 50. 8 books = Rs. 400. -
Q2 Medium
12 men finish work in 6 days. 18 men will finish in:
ExplanationThis is inverse, not direct — trap question. Men × days constant → 12×6 = 18×d → d = 4 days. -
Q3 Easy
If 3 : 5 = 12 : x, x is:
Explanation3x = 60 → x = 20. -
Q4 Easy
Cost varies directly with quantity. 4 kg costs Rs. 120. Cost of 10 kg:
ExplanationRate = 30/kg. 10 kg = Rs. 300. -
Q5 Easy
If a : b = c : d, and a = 8, c = 12, b = 10, then d =
Explanation8/10 = 12/d → d = 15. -
Q6 Medium
6 workers earn Rs. 4,800 in total per day. 9 workers earn:
ExplanationPay proportional to workers: 4800 × 9/6 = Rs. 7,200. -
Q7 Medium
Map scale: 2 cm = 5 km. Distance for 8 cm on map:
Explanation8/2 × 5 = 20 km.
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Q8 Easy
If y varies directly with x and y = 24 when x = 6, y when x = 9:
Explanationy/x = 4. When x = 9, y = 36. -
Q9 Easy
Rs. 45 for 3 pens. Cost of 11 pens:
Explanation15 per pen × 11 = Rs. 165. -
Q10 Medium
If 7 : x = 21 : 30, x equals:
Explanation21x = 210 → x = 10. -
Q11 Easy
Distance traveled varies directly with time at constant speed. In 4 hours, 240 km. In 7 hours:
Explanation60 km/h × 7 = 420 km. -
Q12 Medium
If 2, 5, x, 20 are in proportion, x is:
Explanation2 × 20 = 5x → x = 8. -
Q13 Medium
Printing cost is directly proportional to pages. 50 pages cost Rs. 75. 120 pages cost:
Explanation1.5 per page × 120 = Rs. 180. -
Q14 Easy
If a/b = 3/4 and b = 28, a equals:
Explanationa = 3/4 × 28 = 21.
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DS1 Easy
What is the cost of 10 items?
Statement I5 items cost Rs. 200.
Statement IICost varies directly with quantity.
ExplanationRate = 40/item. 10 items = Rs. 400. -
DS2 Easy
What is the value of x?
Statement I3 : 7 = x : 28.
Statement IIx is a positive integer.
Explanationx = 12 from Statement I.
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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 → 300 km in 5 hours. -
DS4 Medium
What is y when x = 8?
Statement Iy varies directly with x.
Statement IIy = 15 when x = 5.
Explanationy/x = 3. When x = 8, y = 24.