| 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, $$ \left[Time \ taken \ (T) = \frac{l_m + l_s}{s_m}\right] $$ $$ \left[10 = \frac{250 + x}{120}\right] $$ $$ 1200 = 250 + x $$ $$ x = 950 \ m $$