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Aptitude Topics

Basic Concepts

Time and Distance problems form the bedrock of kinematics in quantitative aptitude. The entire topic is built upon a single, intuitive balance: the distance traveled by a moving object depends directly on how fast it moves and how long it travels.

Fundamental Principles

Speed

The rate at which an object covers distance per unit of time. It acts as the scalar magnitude of motion.

Proportionality Rule

When time is constant, distance is directly proportional to speed ($D \propto S$). When speed is constant, distance is directly proportional to time ($D \propto T$). When distance is constant, speed is inversely proportional to time ($S \propto \frac{1}{T}$).

Essential Formulation Tips

  • Always verify that all variables share matching units (e.g., if distance is in kilometers, time must be in hours) before calculating.
  • When distance is fixed, a speed ratio of $a:b$ instantly yields an inverse time ratio of $b:a$.

Shortcut Execution Techniques

  • The Magic Triangle Shortcut: Visualize a triangle with $D$ at the top peak, and $S$ and $T$ side-by-side at the bottom base. Cover the variable you need to find with your hand to reveal its exact formula ($D = S \times T$, $S = \frac{D}{T}$, $T = \frac{D}{S}$).

Contextual Inquiries (FAQs)

Q: What happens to the time required if I double my travel speed over a fixed route?

A: Because speed and time are inversely proportional when distance is constant, doubling your speed cuts your required travel time exactly in half.