SSC CGL Maths: Solved Problems & Detailed Solutions

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Hello there! This is your go-to guide for mastering the mathematics section of the SSC CGL exam. You asked about solved problems with detailed explanations, and I'm here to provide just that. I will break down various types of questions with step-by-step solutions to help you understand the concepts thoroughly and boost your confidence.

Correct Answer

This guide provides solved problems and detailed explanations for the mathematics section of the SSC CGL exam, including arithmetic, algebra, geometry, trigonometry, and data interpretation.

Detailed Explanation

The SSC CGL exam's mathematics section is a critical component, and excelling in this area can significantly improve your overall score. This section covers a wide range of topics, including arithmetic, algebra, geometry, trigonometry, and data interpretation. To ace this section, it’s essential to have a strong grasp of fundamental concepts, practice a variety of problems, and develop effective problem-solving strategies. Let's dive into some solved problems with detailed explanations to help you prepare:

Arithmetic

Arithmetic forms a significant portion of the SSC CGL syllabus. It includes topics like Number System, Simplification, Ratio and Proportion, Percentage, Profit and Loss, Simple and Compound Interest, Time and Work, and Speed, Time, and Distance. Let's explore some problems from this area.

Problem 1: A shopkeeper marks the price of an article 20% above the cost price and then offers a discount of 10%. What is the profit percentage?

Solution:

  1. Assume the Cost Price (CP): Let the cost price of the article be ₹100.
  2. Marked Price (MP): The shopkeeper marks the price 20% above the cost price. Therefore, MP = 100 + (20% of 100) = ₹120.
  3. Discount: The shopkeeper offers a discount of 10% on the marked price. Discount amount = 10% of 120 = ₹12.
  4. Selling Price (SP): SP = MP - Discount = 120 - 12 = ₹108.
  5. Profit: Profit = SP - CP = 108 - 100 = ₹8.
  6. Profit Percentage: Profit % = (Profit / CP) * 100 = (8 / 100) * 100 = 8%.

Answer: The profit percentage is 8%.

Problem 2: A can do a piece of work in 20 days, and B can do the same work in 30 days. In how many days can they complete the work together?

Solution:

  1. Work Done by A in 1 day: A can complete 1/20 of the work in one day.
  2. Work Done by B in 1 day: B can complete 1/30 of the work in one day.
  3. Work Done by A and B Together in 1 day: Together, they can complete 1/20 + 1/30 = (3 + 2) / 60 = 5/60 = 1/12 of the work.
  4. Days to Complete the Work Together: If they complete 1/12 of the work in one day, they will take 12 days to complete the entire work.

Answer: A and B can complete the work together in 12 days.

Algebra

Algebra includes topics such as Simplification, Linear Equations, Quadratic Equations, Exponents and Powers, and Polynomials. Here are some problems from algebra.

Problem 1: Solve for x: 3x + 5 = 20

Solution:

  1. Isolate the term with x: Subtract 5 from both sides of the equation: 3x = 20 - 5 => 3x = 15.
  2. Solve for x: Divide both sides by 3: x = 15 / 3 = 5.

Answer: x = 5.

Problem 2: Simplify: (x + y)^2 - 2xy

Solution:

  1. Expand the square: (x + y)^2 = x^2 + 2xy + y^2.
  2. Simplify: (x^2 + 2xy + y^2) - 2xy = x^2 + y^2.

Answer: x^2 + y^2.

Geometry

Geometry covers topics like Lines and Angles, Triangles, Quadrilaterals, Circles, Mensuration (area and volume), and Coordinate Geometry. Let’s solve a problem.

Problem 1: The length and breadth of a rectangle are 12 cm and 8 cm, respectively. Find its area.

Solution:

  1. Area of a rectangle: Area = Length × Breadth.
  2. Substitute values: Area = 12 cm × 8 cm = 96 sq cm.

Answer: The area of the rectangle is 96 sq cm.

Problem 2: Find the area of a triangle with base 10 cm and height 6 cm.

Solution:

  1. Area of a triangle: Area = 0.5 × Base × Height.
  2. Substitute values: Area = 0.5 × 10 cm × 6 cm = 30 sq cm.

Answer: The area of the triangle is 30 sq cm.

Trigonometry

Trigonometry includes topics such as Trigonometric Ratios, Trigonometric Identities, Heights and Distances. Here’s an example.

Problem 1: If sin θ = 0.5, find the value of θ.

Solution:

  1. Recall the sine values: sin 30° = 0.5.
  2. Therefore: θ = 30°.

Answer: θ = 30°.

Problem 2: Find the value of tan 45°.

Solution:

  1. Recall the tangent value: tan 45° = 1.

Answer: tan 45° = 1.

Data Interpretation

Data Interpretation involves Bar Graphs, Pie Charts, Line Graphs, and Tables. These questions test your ability to analyze and interpret data.

Problem 1:

  • Data: The following table shows the marks obtained by students in a class in different subjects.

    Subject Marks
    Mathematics 80
    Science 75
    English 90
    Social Studies 70
    Hindi 85

  • Question: What is the average marks obtained by the students?

Solution:

  1. Total Marks: 80 + 75 + 90 + 70 + 85 = 400.
  2. Number of Subjects: 5.
  3. Average Marks: Total Marks / Number of Subjects = 400 / 5 = 80.

Answer: The average marks obtained by the students is 80.

Problem 2:

  • Data: A pie chart shows the distribution of expenses in a family.
  • Question: If the family's total income is ₹50,000, and the expenses on food are represented by 30%, what is the expense on food?

Solution:

  1. Expense on Food: 30% of ₹50,000.
  2. Calculate: (30 / 100) × 50,000 = ₹15,000.

Answer: The expense on food is ₹15,000.

Tips for Solving Maths Problems

  • Understand the Concepts: Ensure you have a solid understanding of the fundamental mathematical concepts. Review definitions, formulas, and theorems. Practice solving problems related to each concept.
  • Practice Regularly: Consistent practice is key. Solve a variety of problems from different topics to build your problem-solving skills.
  • Time Management: In the exam, time is crucial. Practice solving problems within a set time limit to improve your speed and accuracy.
  • Use Formulas and Shortcuts: Learn essential formulas and shortcuts to solve problems quickly. Practice applying these formulas to various questions.
  • Learn from Mistakes: Analyze the solutions to the problems you solve. Identify any mistakes you made and understand how to avoid them in the future.
  • Stay Calm and Focused: During the exam, stay calm and focused. Don't panic if you encounter a difficult question. Move on to the next question and come back to the difficult ones later if you have time.
  • Mock Tests: Regularly take mock tests to assess your preparation level and identify areas for improvement. Analyze your performance to understand your strengths and weaknesses.

Key Takeaways

  • Arithmetic: Master topics like percentage, profit and loss, time and work, and interest calculations.
  • Algebra: Focus on solving linear and quadratic equations, and simplification techniques.
  • Geometry: Understand formulas for areas and volumes, and properties of geometric shapes.
  • Trigonometry: Learn trigonometric ratios and identities, and practice problems based on heights and distances.
  • Data Interpretation: Practice analyzing and interpreting data from graphs and charts.
  • Practice: Regularly solve problems, manage time effectively, and learn from mistakes.
  • Mock Tests: Regularly attempt mock tests to assess your preparation.

By following this guide and practicing regularly, you can significantly improve your performance in the mathematics section of the SSC CGL exam. Good luck with your preparation!