Quantitative aptitude
- A sum of money lent at simple interest amounts to Rs. 7,800 in 3 years and to Rs. 9,000 in 5 years. What is the rate of interest per annum? Answer: B. 10% Answer: (B) 10% Interest for 2 years = 9000 − 7800 = 1200, so Rs. 600 per year. Principal = 7800 − 3 × 600 = 6000. Rate = 600... 1
- What is the compound interest on Rs. 16,000 at 10% per annum for 3 years, compounded annually (in Rs.)? Answer: C. 5296 Answer: (C) 5296 Amount = 16000 × (1.1)³ = 21296 . CI = 21296 − 16000 = Rs. 5,296. 1
- A and B together can finish a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can A, B and C together finish it? Answer: C. 10 Answer: (C) 10 2(A + B + C) = 1/12+1/15+1/20 = 12/60 = 1/5 . So A + B + C = 1/10 : 10 days. 1
- Two trains, 150 m and 210 m long, run on parallel tracks in opposite directions at 45 km/h and 63 km/h. How many seconds do they take to cross each other completely? Answer: A. 12 Answer: (A) 12 Relative speed = 108 km/h = 30 m/s. Distance = 150 + 210 = 360 m. Time = 360 ÷ 30 = 12 s. 1
- Walking at 5 km/h, a man reaches his office 10 minutes late. Walking at 6 km/h, he reaches 5 minutes early. What is the distance to his office (in km)? Answer: B. 7.5 Answer: (B) 7.5 The time difference is 15 min = 1/4 h. d/5 - d/6 = d/30 = 1/4 , so d = 7.5 km. 1
- What will come in place of the question mark (?) in the series?3, 8, 18, 38, 78, ? Answer: B. 158 Answer: (B) 158 Each term = previous × 2 + 2. 78 × 2 + 2 = 158. 1
- What will come in place of the question mark (?) in the series?5, 6, 14, 45, 184, ? Answer: D. 925 Answer: (D) 925 Pattern: ×1 + 1, ×2 + 2, ×3 + 3, ×4 + 4, so next = 184 × 5 + 5 = 925. 1
- What will come in place of the question mark (?) in the series?120, 119, 115, 106, 90, ? Answer: C. 65 Answer: (C) 65 Subtract squares: −1, −4, −9, −16, −25. 90 − 25 = 65. 1
- What will come in place of the question mark (?) in the series?6, 7, 15, 42, 106, ? Answer: D. 231 Answer: (D) 231 Add cubes: +1, +8, +27, +64, +125. 106 + 125 = 231. 1
- Find the wrong number in the series.2, 6, 15, 31, 56, 93 Answer: A. 93 Answer: (A) 93 Differences should be 2², 3², 4², 5², 6² = 4, 9, 16, 25, 36: 2, 6, 15, 31, 56, 92. So 93 is wrong. 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. \( x^2 - 9x + 20 = 0 \)II. \( y^2 - 15y + 56 = 0 \) Answer: B. x < y Answer: (B) x < y I gives x = 4, 5. II gives y = 7, 8. 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. \( x^2 + 3x - 28 = 0 \)II. \( y^2 - 2y - 15 = 0 \) 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
- What will come in place of the question mark (?)?\( 45\% \text{ of } 860 - 12^2 + 17 \times 8 = ? \) Answer: C. 379 Answer: (C) 379 387 - 144 + 136 = 379 . 1
- What will come in place of the question mark (?)?\( ? \div 16 \times 4.5 = 27 \times 3 \) Answer: C. 288 Answer: (C) 288 ? = 81 × 16/4.5 = 288 . 1
- What will come in place of the question mark (?)?\( (\sqrt{2025} + \sqrt{576}) \times 4 - 99 = ? \) Answer: A. 177 Answer: (A) 177 (45 + 24) × 4 - 99 = 276 - 99 = 177 . 1
- What approximate value will come in place of the question mark (?)?\( 39.89\% \text{ of } 1499.8 - 22.03 \times 8.98 + 539.7 \div 17.96 = ? \) Answer: A. 432 Answer: (A) 432 Round: 40% of 1500 - 22 × 9 + 540 ÷ 18 = 600 - 198 + 30 = 432 (exact ≈ 430.5). 1
- What approximate value will come in place of the question mark (?)?\( (12.03)^2 + (6.98)^3 - 299.9 \div 5.02 = ? \) Answer: D. 427 Answer: (D) 427 Round: 12² + 7³ - 300 ÷ 5 = 144 + 343 - 60 = 427 (exact ≈ 425.0). 1
- The present ages of A and B are in the ratio 5 : 7. Six years ago, their ages were in the ratio 2 : 3. What is B's present age (in years)? Answer: D. 42 Answer: (D) 42 Let ages be 5k and 7k. 5k-6/7k-6 = 2/3 ⇒ 15k - 18 = 14k - 12 ⇒ k = 6 . B = 42 years. 1
- The average of five numbers is 42. When one number is removed, the average of the remaining four numbers becomes 40. What is the number removed? Answer: D. 50 Answer: (D) 50 Sum of five = 210, sum of four = 160. Removed number = 210 − 160 = 50. 1
- A boat covers 48 km downstream in 3 hours and 32 km upstream in 4 hours. What is the speed of the boat in still water (in km/h)? Answer: B. 12 Answer: (B) 12 Downstream speed = 16 km/h, upstream = 8 km/h. Speed in still water = (16 + 8) ÷ 2 = 12 km/h. 1
- Two numbers are in the ratio 3 : 4 and their LCM is 180. What is the sum of the two numbers? Answer: D. 105 Answer: (D) 105 Let the numbers be 3k and 4k (HCF k). LCM = 12k = 180, so k = 15. Numbers are 45 and 60; sum = 105. 1
- The perimeter of a rectangle is 64 cm and its length is 6 cm more than its breadth. What is its area (in sq cm)? Answer: C. 247 Answer: (C) 247 l + b = 32 and l − b = 6, so l = 19 cm, b = 13 cm. Area = 19 × 13 = 247 sq cm. 1
- A 60-litre mixture contains milk and water in the ratio 7 : 3. How many litres of water must be added to make the ratio 3 : 2? Answer: D. 10 Answer: (D) 10 Milk = 42 L, water = 18 L. Need 42 : (18 + w) = 3 : 2, so 18 + w = 28 and w = 10 L. 1
- The sum of three consecutive even numbers is 138. What is the largest of the three numbers? Answer: C. 48 Answer: (C) 48 Middle number = 138 ÷ 3 = 46. The numbers are 44, 46, 48, so the largest is 48. 1