# Train and Platform Aptitude Formulas, Definitions, & Tricks:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Time Speed and Distance Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

We are discussing different cases of trains and platforms here to understand the scenario easily.

Case (2): When a moving object (may be train) is crossing a stationary object (may be platform) and length of stationary object is not considered. Then $$\left[T = \frac{l_m}{s_m}\right]$$

Where,
$$T$$ = Time taken.
$$l_m$$ = Length of moving object.
$$s_m$$ = Speed of moving object.

Example (1): A $$200 \ m$$ long train is crossing a $$70 \ m$$ platform, at the speed of $$150 \ km/hr$$. If length of the platform is not considered then How much time the train will take to cross the platform?

Solution: Given values, Length of the train $$(l_m) = 200 \ meter$$, length of the platform $$(l_s) = 70 \ meter$$, and Speed of the train $$(s_m) = 150 km/hr$$ = $$150 \times \frac{5}{18}$$ meter/sec, then $$\left[Time \ taken \ (T) = \frac{l_m}{s_m}\right]$$ $$\left[Time \ taken \ (T) = \frac{200}{150 \times \frac{5}{18}}\right]$$ $$Time \ taken \ (T) = \frac{200 \times 18}{750} = 4.8 \ sec$$

Example (2): If a $$350 \ m$$ long train takes $$12 \ sec$$ to cross a $$90 \ m$$ platform, then find the speed of the train? where as the length of the platform is not considered.

Solution: Given values, Length of the train $$(l_m) = 350 \ meter$$, length of the platform $$(l_s) = 90 \ meter$$, and time taken by the train to cross the train $$(T) = 12 \ sec$$, then $$\left[Time \ taken \ (T) = \frac{l_m}{s_m}\right]$$ $$\left[12 = \frac{350}{s_m}\right]$$ $$speed \ (s_m) = \frac{350}{12} = 29.167 \ m/sec$$

Example (3): If a train takes $$20 \ sec$$ to cross a $$75 \ m$$ platform at the speed of $$120 \ m/sec$$, then find the length of the train? where as the length of the platform is not considered.

Solution: Given values, length of the platform $$(l_s) = 75 \ meter$$, and time taken by the train to cross the train $$(T) = 20 \ sec$$, speed of the train $$s_m = 120 \ m/sec$$ then $$\left[Time \ taken \ (T) = \frac{l_m}{s_m}\right]$$ $$\left[20 = \frac{l_m}{120}\right]$$ $$length \ of \ train \ (l_m) = 2400 \ m$$

Example (4): If a $$250 \ m$$ long train takes $$10 \ sec$$ to cross a $$x \ m$$ platform at the speed of $$150 \ m/sec$$, then find the value of $$x$$? where as the length of the platform is not considered.

Solution: Given values, Length of the train $$(l_m) = 250 \ meter$$, length of the platform $$(l_s) = x \ meter$$, and time taken by the train to cross the train $$(T) = 10 \ sec$$, speed of the train $$s_m = 150 \ m/sec$$ then from the previous chapter when the length of platform is considered, $$\left[Time \ taken \ (T) = \frac{l_m + l_s}{s_m}\right]$$ $$\left[10 = \frac{250 + x}{120}\right]$$ $$1200 = 250 + x$$ $$x = 950 \ m$$