Numerical Ability: Simple and Compound Interest

Numerical Ability

• Numerical ability encompasses various mathematical skills, including calculation, problem-solving, and data interpretation.
• It involves applying arithmetic operations, algebraic principles, and geometrical concepts to solve quantitative problems.
• Practicing numerous problems is crucial for improving numerical ability.

Simple Interest

• Simple interest is calculated on the principal amount only.
• Formula: Simple Interest = (Principal × Rate × Time) / 100
• SI = (P × R × T) / 100, where:
  • P = Principal amount
  • R = Rate of interest (per annum)
  • T = Time period (in years)
• Used for short-term loans or investments.
• Important to understand the components and calculations using the formula.

Compound Interest

• Compound interest is calculated on the principal and accumulated interest from previous periods.
• Formula for Compound Interest on the principal amount:
  • Amount = P (1 + r/n)^(nt)
  • where,
    • P = Principal amount
    • r = Rate of interest per annum
    • n = Number of times interest is compounded per year
    • t = Time period in years
• It results in faster growth compared to simple interest.
• Understanding the compounding frequency is critical.

Height and Distance

• Problems involve finding heights or distances using trigonometric ratios, like sine, cosine, and tangent.
• Visualizing geometrical figures and their right-angled triangles is vital.
• Using trigonometric ratios to find unknown heights, distances, or angles.
• Applying appropriate ratios to solve the problems step-by-step.

Problems on Trains

• These problems involve calculating the time taken for a train to pass a certain point, object, or another train.
• Understanding the relative speeds of the objects is key.
  • The relative speed is the sum of the speeds when the trains are moving in opposite directions and the difference of the speeds when the trains are moving in the same direction.
• Important to correctly determine the relative speed based on motion.
• Relevant formulas: Distance = Speed × Time, and concepts about relative speeds
  • Calculating distances, times, and speeds.

Time and Speed

• Time and speed problems deal with the relationship between time, speed, and distance.
• Basic formula: Speed = Distance / Time
  • Time = Distance / Speed
  • Distance = Speed × Time
• Problems often involve converting units of time and distance (e.g., kilometers to meters, hours to minutes).
• Solving problems requires understanding the relationships and applying the relevant formulas.
• Incorporates concepts like average speed, and problems with varying speed.