Practice Ratio & Proportion MCQs for GBPSC Junior Clerk (BS-9) Mathematics — topic-wise sets with solved answers.
Q1. The ratio of the area of a square to that of the square drawn on its diagonal is?
Answer: 1:02
Explanation: If the square has side a, its diagonal is a√2; ratio of areas = a² : (a√2)² = 1 : 2.
Q2. If A : B : C = 2 : 3 : 4, what is the ratio A/B : B/C : C/A?
Answer: 8:09:24
Explanation: A/B = 2/3, B/C = 3/4, C/A = 4/2 = 2; converting to common denominator gives ratio 8 : 9 : 24.
Q3. The ratio of the prices of three articles X, Y and Z is 8 : 5 : 3. If the prices of X, Y and Z are increased by 25%, 20% and 33 1/3% respectively, then what would be the ratio of the new prices of X, Y and Z?
Answer: 5:03:02
Explanation: New prices: X = 8×1.25 = 10, Y = 5×1.20 = 6, Z = 3×(4/3) = 4; ratio = 10 : 6 : 4 = 5 : 3 : 2.
Q4. A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is_________?
Answer: 01-Mar
Explanation: Equal volumes: πr²h = (1/3)πr²H → h/H = 1/3, so the ratio of cylinder height to cone height is 1 : 3.
Q5. What is the mean proportional of 4 and 16?
Answer: ±8
Explanation: The correct value is ±8. Apply the formula or arithmetic step shown in the question and
Q6. In Faisalabad, ratio of bicycles and motorcycles in 2 : 3. If bicycles increase by 15% and motorcycles increase by 20%, what is overall percent increase in both cycles and motorcycles?
Answer: 18%
Explanation: Taking bicycles = 2k and motorcycles = 3k, new total = 2.3k + 3.6k = 5.9k; increase over 5k = 0.9k/5k = 18%.
Q7. 1.272747.... is a/an
Answer: Irrational Number
Explanation: A non-terminating, non-repeating decimal cannot be expressed as a ratio of two integers, so it is an irrational number.
Q8. The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:_______?
Answer: Rs. 18
Explanation: Weighted average = (2×15 + 3×20)/5 = (30+60)/5 = Rs.18 per kg.
Q9. A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain is Rs.18000. Then, A's share is?
Answer: Rs0.60
Explanation: Profit shares: A = P×12, B = 2P×6 = 12P, C = 3P×4 = 12P; ratio = 1:1:1; A's share = 18000/3 = Rs.6,000.
Q10. The sum of cubes of two numbers is 280. If the numbers are in the ratio 2:3, find the smallest number.
Answer: 4
Explanation: Let numbers be 2x and 3x; (2x)³ + (3x)³ = 8x³ + 27x³ = 35x³ = 280 → x = 2; smallest number = 2×2 = 4.
Q11. The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A?
Answer: Rs. 504000
Explanation: C = Rs.15,000; B = 15000 × 1.12 = Rs.16,800; A = 16800 × 5/2 = Rs.42,000/month; annual = Rs.5,04,000.
Q12. what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Answer: 5:06
Explanation: By alligation: (8.75 − 7.50) : (7.50 − 6.00) = 1.25 : 1.50 = 5 : 6; ratio of cheaper to costlier = 5:6.
Q13. The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is__________?
Answer: 48
Explanation: Numbers are 3×4 = 12 and 4×4 = 16; LCM = 48.
Q14. The ratio of the length of a rod to its shadow is 1:√3. What is the angle of elevation of the sun?
Answer: 30°
Explanation: The correct value is 30°. Apply the formula or arithmetic step shown in the question and
Q15. What is the price of a 12x6 carpet if an 8x3 carpet costs Rs. 6,288, assuming price is proportional to area? proportion
Answer: Rs. 18864
Explanation: Area ratio = (12×6)/(8×3) = 3; price = 3 × 6288 = Rs.18,864.
Q16. A fruit basket contains oranges, peaches, and strawberries in the ratio 2:3:4. If there are 8 oranges, how many total fruit items are in the basket?
Answer: 36
Explanation: Ratio 2:3:4 with 8 oranges means 1 part = 4; total parts = 9; total fruits = 9×4 = 36.
Q17. A sum of Rs.427 is to be divided among A,B, and C in such a way that 3 times A's share, 4 times B's share and 7 times C's share are all equal. The Share of C is:
Answer: Rs. 84
Explanation: 3A = 4B = 7C = k; A = k/3, B = k/4, C = k/7; total = k(28+21+12)/84 = 61k/84 = 427 → k = 588; C's share = 588/7 = Rs. 84.
Q18. Two bikes start at the same time from two destinations 300 km apart and travel towards each other. If they cross each other at a distance of 130 km from one of the destinations, what is the ratio of their speeds?
Answer: 13:17
Explanation: The two bikes cover 130 km and 170 km respectively; ratio of speeds = 130:170 = 13:17.
Q19. x is 20% more than z and y is 80% more than z. Find x:y.
Answer: 2:03
Explanation: x = 1.2z, y = 1.8z; x:y = 1.2:1.8 = 2:3. Show the calculation clearly when solving similar quantitative items.
Q20. The ratio of two numbers is 5:9. If each number is decreased by 5, the ratio becomes 5:11. Find the numbers.
Answer: 15, 27
Explanation: 5x/(9x) ratio reduced by 5 each: (5x−5)/(9x−5)=5/11; cross-multiplying: 55x−55=45x−25; x=3; numbers = 15 and 27.
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