QB_PH_GA_016: Quantitative Aptitude

A train of length $180\text{ meters}$ traveling at a uniform speed of $72\text{ km/h}$ crosses a railway platform in $24\text{ seconds}$. What is the length of the platform in meters?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Speed Unit Conversion**: $v = 72\text{ km/h} = 72 \times \frac{5}{18}\text{ m/s} = 20\text{ m/s}$ 2. **Total Distance Covered** in crossing the platform: $D = L_{\text{train}} + L_{\text{platform}}$ 3. **Kinematics Equation**: $D = v \times t = 20\text{ m/s} \times 24\text{ s} = 480\text{ m}$ 4. **Isolating Platform Length**: $L_{\text{platform}} = 480\text{ m} - 180\text{ m} = 300\text{ m}$ 5. **Official Answer**: 300.