Quantitative aptitude
- In the following question, two equations numbered I and II are given. Solve both equations and choose the correct relationship between x and y.I. \( x^2 + 9x + 20 = 0 \)II. \( y^2 + 5y + 6 = 0 \) Answer: B. x < y Answer: (B) x < y I gives x = -5, -4. II gives y = -3, -2. Comparing every pair of values: x < y. 1
- In the following question, two equations numbered I and II are given. Solve both equations and choose the correct relationship between x and y.I. \( x^2 - 13x + 42 = 0 \)II. \( y^2 - 11y + 30 = 0 \) Answer: B. x ≥ y Answer: (B) x ≥ y I gives x = 6, 7. II gives y = 5, 6. Comparing every pair of values: x ≥ y. 1
- In the following question, two equations numbered I and II are given. Solve both equations and choose the correct relationship between x and y.I. \( 2x^2 - 7x + 3 = 0 \)II. \( 2y^2 - 9y + 10 = 0 \) Answer: D. x = y or the relationship between x and y cannot be established Answer: (D) x = y or the relationship between x and y cannot be e... 1
- In the following question, two equations numbered I and II are given. Solve both equations and choose the correct relationship between x and y.I. \( x^2 + 7x + 12 = 0 \)II. \( y^2 + 5y + 6 = 0 \) Answer: C. x ≤ y Answer: (C) x ≤ y I gives x = -4, -3. II gives y = -3, -2. Comparing every pair of values: x ≤ y. 1
- What will come in place of the question mark (?)?\( 35\% \text{ of } 640 + 18^2 - 25 \times 6 = ? \) Answer: C. 398 Answer: (C) 398 224 + 324 - 150 = 398 . 1
- What will come in place of the question mark (?)?\( \left(\tfrac{3}{4} \text{ of } 896\right) \div 12 + ? = 85 \) Answer: D. 29 Answer: (D) 29 3/4 × 896 = 672;\ 672 ÷ 12 = 56;\ ? = 85 - 56 = 29 . 1
- What will come in place of the question mark (?)?\( \sqrt{1764} + 3^3 \times 4 - 15\% \text{ of } 300 = ? \) Answer: A. 105 Answer: (A) 105 42 + 108 - 45 = 105 . 1
- What approximate value will come in place of the question mark (?)?\( 24.97\% \text{ of } 799.8 + 14.02 \times 11.96 - 1260.2 \div 35.1 = ? \) Answer: D. 332 Answer: (D) 332 Round: 25% of 800 + 14 × 12 - 1260 ÷ 35 = 200 + 168 - 36 = 332 (exact value ≈ 331.5). 1
- What approximate value will come in place of the question mark (?)?\( \sqrt{624.8} \times 7.99 + 47.9\% \text{ of } 450.2 - ? = 260 \) Answer: D. 156 Answer: (D) 156 Round: 25 × 8 + 48% of 450 = 200 + 216 = 416 ; ? = 416 - 260 = 156 (exact ≈ 155.4). 1
- What is 72 km/h in metres per second? Answer: A. 20 m/s Answer: (A) 20 m/s Multiply by 5/18 : 72 × 5/18 = 20 m/s. 1
- A car covers 360 km in 4 hours 30 minutes. What is its speed? Answer: B. 80 km/h Answer: (B) 80 km/h 4 h 30 min = 4.5 h. Speed = 360 ÷ 4.5 = 80 km/h. 1
- A train 240 m long runs at 54 km/h. How long does it take to pass a signal pole? Answer: D. 16 seconds Answer: (D) 16 seconds 54 km/h = 15 m/s. Time = length ÷ speed = 240 ÷ 15 = 16 seconds. 1
- A train 150 m long running at 72 km/h crosses a platform 250 m long. How long does it take? Answer: D. 20 seconds Answer: (D) 20 seconds Distance = train + platform = 400 m. 72 km/h = 20 m/s. Time = 400 ÷ 20 = 20 seconds. Trap: 7.5... 1
- A man walks at 5 km/h for 3 hours and then at 6 km/h for 2 hours. What is his average speed for the whole walk? Answer: C. 5.4 km/h Answer: (C) 5.4 km/h Total distance = 15 + 12 = 27 km in 5 hours. Average speed = 27 ÷ 5 = 5.4 km/h. Trap: 5.5 is the pl... 1
- Two trains 120 m and 130 m long run in opposite directions at 40 km/h and 50 km/h. How long do they take to cross each other completely? Answer: A. 10 seconds Answer: (A) 10 seconds Opposite directions: relative speed = 90 km/h = 25 m/s. Distance = 120 + 130 = 250 m. Time = 25... 1
- The speeds of A and B are in the ratio 3 : 4. What is the ratio of the times they take to cover the same distance? Answer: D. 4 : 3 Answer: (D) 4 : 3 For a fixed distance, time is inversely proportional to speed. Time ratio = 4 : 3. 1
- A car covers a distance in 3 hours at 40 km/h. At what speed must it travel to cover the same distance in 2 hours 30 minutes? Answer: C. 48 km/h Answer: (C) 48 km/h Distance = 40 × 3 = 120 km. Speed = 120 ÷ 2.5 = 48 km/h. 1
- Walking at \(\frac{3}{4}\) of his usual speed, a man reaches his office 20 minutes late. What is his usual time to reach the office? Answer: A. 60 minutes Answer: (A) 60 minutes At 3/4 the speed he takes 4/3 the time. The extra 1/3 of the usual time = 20 min. Usual time =... 1
- A boy walking at 5 km/h reaches school 7 minutes late. Walking at 6 km/h he reaches 5 minutes early. How far is the school? Answer: C. 6 km Answer: (C) 6 km The difference in time = 7 + 5 = 12 min = 1/5 h. Shortcut: d = S₁ S₂/S₂ - S₁ × time difference = 5 × 6/1 ×... 1
- A train passes a pole in 15 seconds and a 100 m long platform in 25 seconds. What is the length of the train? Answer: B. 150 m Answer: (B) 150 m The extra 100 m (platform) takes 25 − 15 = 10 s, so speed = 10 m/s. Length = 10 × 15 = 150 m. 1
- Two trains 140 m and 160 m long run on parallel tracks in the same direction at 60 km/h and 42 km/h. How long will the faster train take to pass the slower one completely? Answer: D. 60 seconds Answer: (D) 60 seconds Same direction: relative speed = 60 − 42 = 18 km/h = 5 m/s. Distance = 140 + 160 = 300 m. Time... 1
- A policeman is 150 m behind a thief. The thief runs at 8 km/h and the policeman chases him at 10 km/h. How far will the thief have run before he is caught? Answer: B. 600 m Answer: (B) 600 m The gap closes at 2 km/h. Time = 0.15 ÷ 2 = 0.075 h. Thief's distance = 8 × 0.075 = 0.6 km = 600 m. Short... 1
- Two cars start at the same time from towns A and B, 360 km apart, and move towards each other at 50 km/h and 40 km/h. How far from A do they meet? Answer: D. 200 km Answer: (D) 200 km Time to meet = 360 ÷ (50 + 40) = 4 h. The car from A covers 50 × 4 = 200 km. 1
- A man covers three equal distances at 10 km/h, 20 km/h and 60 km/h. What is his average speed for the whole journey? Answer: B. 18 km/h Answer: (B) 18 km/h Take each distance = 60 km (LCM). Times = 6 h + 3 h + 1 h = 10 h for 180 km. Average speed = 180 ÷ 10... 1