Numerical Aptitude is one of the most crucial sections in competitive exams like APSRTC recruitment tests. It assesses a candidate’s ability to solve problems using mathematical concepts and logical reasoning within a limited time. Mastering this section not only boosts your overall score but also enhances your problem-solving skills, which are essential for various government job roles.
1. Percentages
Q1. If a number is increased by 20%, it becomes 240. What is the original number?
A.
Let the number be x.
Then,
x + 20% of x = 240
⇒ x(1 + 20/100) = 240
⇒ x × 1.2 = 240
⇒ x = 240 / 1.2 = 200
2. Time and Distance
Q2. A bus covers 240 km in 4 hours. What is its speed?
A.
Speed = Distance / Time = 240 / 4 = 60 km/h
3. Profit and Loss
Q3. A man buys an item for ₹500 and sells it for ₹600. What is the profit percentage?
A.
Profit = 600 – 500 = ₹100
Profit% = (100 / 500) × 100 = 20%
4. Averages
Q4. The average of five numbers is 64. If one of the numbers is 80, what is the average of the remaining four numbers?
A.
Total of 5 numbers = 64 × 5 = 320
Remaining total = 320 – 80 = 240
Average of remaining 4 = 240 / 4 = 60
5. Simple Interest
Q5. What is the simple interest on ₹1,000 at 5% per annum for 3 years?
A.
SI = (P × R × T) / 100 = (1000 × 5 × 3) / 100 = ₹150
6. Ratio and Proportion
Q6. Divide ₹600 in the ratio 2:3.
A.
Sum of ratio = 2 + 3 = 5
Part 1 = (2/5) × 600 = ₹240
Part 2 = (3/5) × 600 = ₹360
7. Number Series
Q7. What is the next number in the series: 2, 4, 8, 16,?
A.
This is a ×2 series: Next = 16 × 2 = 32
8. Problems on Ages
Q8. A father is 30 years older than his son. If the son is 10 years old, what will be the father’s age after 5 years?
A.
Father’s current age = 10 + 30 = 40
After 5 years: 40 + 5 = 45 years
9. Pipes and Cisterns
Q9. Pipe A can fill a tank in 4 hours, and Pipe B in 6 hours. If both are opened together, in how much time will the tank be full?
A.
Work per hour = (1/4 + 1/6) = (3 + 2)/12 = 5/12
Time = 12/5 = 2.4 hours or 2 hours 24 minutes
10. Mixture and Alligation
Q10. In what ratio must water be mixed with milk worth ₹20/litre so that the mixture is worth ₹16/litre?
A.
Milk : Water = (20 – 16) : (16 – 0) = 4 : 16 = 1 : 4
21. Percentage
Q21. What is 25% of 480?
A. (25/100) × 480 = 120
22. Average
Q22. The average of 7, 9, 12, and 17 is:
A. (7 + 9 + 12 + 17) / 4 = 45 / 4 = 11.25
23. Ratio
Q23. If A : B = 3 : 4 and B : C = 5 : 6, then A : C = ?
A. A : B = 3 : 4, B : C = 5 : 6 → Multiply:
A : B : C = 15 : 20 : 24 → A : C = 15 : 24 = 5 : 8
24. Number System
Q24. Find the least number which, when divided by 3, 4, 5, and 6, leaves a remainder 2 in each case.
A. LCM of 3, 4, 5, 6 = 60
Required number = 60 + 2 = 62
25. Time & Distance
Q25. If speed is 60 km/h, how much time is needed to travel 90 km?
A. Time = Distance / Speed = 90 / 60 = 1.5 hours or 1 hour 30 minutes
26. Profit & Loss
Q26. Cost Price = ₹250, Selling Price = ₹200, find loss %.
A. Loss = ₹50 → Loss% = (50/250)×100 = 20%
27. Pipes & Cisterns
Q27. A pipe fills a tank in 5 hours. How much of the tank is filled in 2 hours?
A. 2/5 = 0.4
28. Simplification
Q28. Simplify: 8 + 4 × 2 − 6 ÷ 3 = ?
A. 8 + 8 − 2 = 14
29. Ages
Q29. The present age of a father is 3 times that of his son. After 5 years, the father will be twice as old as his son. Find the son’s current age.
A. Let son = x → father = 3x
After 5 years: 3x + 5 = 2(x + 5) → 3x + 5 = 2x + 10 → x = 5
30. Interest
Q30. Simple interest on ₹1200 at 5% p.a. for 2 years =?
A. SI = (1200×5×2)/100 = ₹120
31. Boats & Streams
Q31. A boat’s speed in still water is 10 km/h. If the current speed is 2 km/h, find the downstream speed.
A. 10 + 2 = 12 km/h
32. Train
Q32. A train travels at 72 km/h. Find the speed in m/s.
A. 72 × (1000/3600) = 20 m/s
33. Algebra
Q33. If x = 3, find the value of x² + 2x + 1.
A. 9 + 6 + 1 = 16
34. Geometry (Area)
Q34. Area of a triangle with base 10 cm and height 8 cm =?
A. (1/2)×10×8 = 40 cm²
35. Calendar
Q35. If March 1, 2023, is a Wednesday, what day is March 1, 2024?
2024 is a leap year, so add 2 days → Friday
36. Mixture
Q36. A mixture has milk and water in a 7:3 ratio. What is % of milk?
A. (7/10) × 100 = 70%
37. Time & Work
Q37. A can do a job in 12 days, B in 18 days. Working together, how many days?
A. 1/12 + 1/18 = 5/36 → Time = 36/5 = 7.2 days
38. Fractions
Q38. 2/5 + 3/10 = ?
A. = (4 + 3)/10 = 7/10
39. Simple Equation
Q39. Solve: 2x + 5 = 19
A. 2x = 14 → x = 7
40. Volume
Q40. Volume of a cube with a side of 5 cm =?
A. 5³ = 125 cm³
Conclusion
Numerical Aptitude is a high-scoring and crucial section in the APSRTC competitive exams. With regular practice, a strong grasp of basic mathematical concepts, and the application of shortcuts and strategies, candidates can significantly improve their speed and accuracy.
Success in this section not only improves your overall exam score but also enhances your logical thinking and problem-solving abilities—skills that are essential for any position in Andhra Pradesh State Road Transport Corporation or other government sectors.
