Problem Solving – Study Notes for Competitive Exams
Problem Solving is a key part of Quantitative Aptitude in exams such as Banking, SSC, Railways, Insurance, Defence, and State-level exams. This section tests a candidate’s ability to apply logical thinking, basic mathematics, and quick calculation skills.
What is Problem Solving?
Problem Solving involves questions based on real-life situations where candidates must analyze given data and find the correct solution using mathematical concepts.
Common Topics in Problem Solving
- Age problems
- Average
- Ratio and Proportion
- Time and Work
- Time and Distance
- Profit and Loss
- Simple and Compound Interest
- Mixtures and Allegations
- Number-based word problems
How to Score Well in Problem Solving
- Understand the concept, not just formulas
- Practice short tricks and approximations
- Improve calculation speed
- Read questions carefully before solving
Regular practice of problem-solving questions helps improve accuracy, speed, and confidence, which is essential for clearing competitive exams.
📝 Top 25 Problem Solving Questions
- The sum of two numbers is 40 and their difference is 10. Find the larger number.
- The average of 5 numbers is 20. What is their total sum?
- If 3 pens cost ₹45, what is the cost of 7 pens?
- A man buys an article for ₹800 and sells it for ₹920. Find the profit.
- The ratio of two numbers is 3:5 and their sum is 64. Find the numbers.
- A train travels 120 km in 2 hours. Find its speed.
- If A can do a work in 10 days, how many days will he take to do half the work?
- Find 25% of 640.
- The simple interest on ₹1000 for 2 years at 10% per annum is?
- The perimeter of a square is 48 cm. Find the length of one side.
- A shopkeeper gives a discount of 10% on ₹500. Find the selling price.
- The sum of angles of a triangle is?
- If 12 workers can complete a work in 15 days, how many days will 6 workers take?
- Find the LCM of 6 and 8.
- Find the HCF of 18 and 24.
- The average age of 4 persons is 25 years. Find their total age.
- If the cost price is ₹400 and profit is ₹100, find the selling price.
- A car travels 60 km at a speed of 30 km/h. Find the time taken.
- What is the square of 15?
- If x + 5 = 12, find x.
- Find the value of 3² + 4².
- What is 20% of 250?
- The difference between two numbers is 15 and the smaller number is 25. Find the larger number.
- If the radius of a circle is 7 cm, find its diameter.
- How many minutes are there in 2.5 hours?