# Train and Platform Aptitude Questions:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Time Speed and Distance Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. Two trains x and y, start moving at the same time from stations A and B respectively towards each other. After passing each other, trains take $$20 \ hours$$ and $$5 \ hours$$ to reach stations A and B respectively. If the train x is moving at the speed of $$65 \ km/hr$$, then find the speed of the train y?

1. $$125 \ km/hr$$
2. $$135 \ km/hr$$
3. $$130 \ km/hr$$
4. $$120 \ km/hr$$

Answer: (c) $$130 \ km/hr$$

Solution: Given, speed of the train x $$(s_1) = 65 \ km/hr$$
time taken by the train x to reach the station B $$(T_1) = 20 \ hours$$
time taken by the train y to reach the station A $$(T_2) = 5 \ hours$$, then $$\frac{s_1}{s_2} = \sqrt{\frac{T_2}{T_1}}$$ $$\frac{65}{s_2} = \sqrt{\frac{5}{20}}$$ $$\frac{65}{s_2} = \sqrt{\frac{1}{4}}$$ $$\frac{65}{s_2} = \frac{1}{2}$$ $$s_2 = 130 \ km/hr$$

1. A train crossed a pole in $$10 \ seconds$$, if the length of the train is $$260 \ meter$$, then find the speed of the train?

1. $$28 \ m/sec$$
2. $$26 \ m/sec$$
3. $$25 \ m/sec$$
4. $$24 \ m/sec$$

Answer: (b) $$26 \ m/sec$$

Solution: Given, length of the train $$(l_m) = 260 \ meter$$
time taken by the train to cross the train $$(T) = 10 \ seconds$$, then $$time \ taken \ (T) = \frac{l_m}{s_m}$$ $$10 = \frac{260}{s_m}$$ $$s_m = 26 \ m/sec$$

1. A man goes from station A to station B at the speed of $$40 \ km/hr$$ and returns from station B to station A at the speed of $$60 \ km/hr$$. If the man takes $$20 \ hours$$ on traveling then find the distance between station A and B?

1. $$435 \ km$$
2. $$475 \ km$$
3. $$465 \ km$$
4. $$480 \ km$$

Answer: (d) $$480 \ km$$

Solution: Given, speed of the man from station A to B = $$40 \ km/hr$$
speed of the man from station B to A = $$60 \ km/hr$$
time taken by the man on traveling = $$20 \ hours$$
Let the distance between between the two stations = $$d \ km$$, then $$\frac{d}{40} + \frac{d}{60} = 20$$ $$d \ \left(\frac{1}{40} + \frac{1}{60}\right) = 20$$ $$d \ \left(\frac{3 + 2}{120}\right) = 20$$ $$d = \frac{120 \times 20}{5} = 480 \ km$$

1. A train crossed a pole at the speed of $$45 \ km/hr$$. If the length of the train is $$80 \ meter$$, then find the time taken by the train tp cross the pole? where as the length of the pole is not considered.

1. $$6.4 \ seconds$$
2. $$5.6 \ seconds$$
3. $$5.8 \ seconds$$
4. $$6.9 \ seconds$$

Answer: (a) $$6.4 \ seconds$$

Solution: Given, speed of the train $$(s_m) = 45 \ km/hr = 45 \times \frac{5}{18} \ m/sec$$
length of the train $$(l_m) = 80 \ meter$$, then $$time \ taken \ (T) = \frac{l_m}{s_m}$$ $$= \frac{80}{45 \times \frac{5}{18}}$$ $$= \frac{80 \times 18}{45 \times 5}$$ $$= \frac{1440}{225} = 6.4 \ sec$$

1. Two trains x and y, start moving at the same time from station A and B respectively towards each other. The train x is moving at the speed of $$45 \ km/hr$$ and the train y is moving at the speed of $$55 \ km/hr$$. If the distance between two stations A and B is $$500 \ km$$, then find how far from station A both the trains will cross each other?

1. $$250 \ km$$
2. $$225 \ km$$
3. $$265 \ km$$
4. $$230 \ km$$

Answer: (b) $$225 \ km$$

Solution: Given, distance between two stations = $$500 \ km$$
speed of the train x = $$45 \ km/hr$$
speed of the train y = $$55 \ km/hr$$
time taken by the trains to meet each other = $$\frac{500}{45 + 55}$$ = $$5 \ hours$$
distance from station A when both the trains will cross each other $$= 5 \times 45 = 225 \ km$$

1. A man crosses a $$250 \ meter$$ long bridge in $$3 \ minutes$$, then find the speed of the man?

1. $$1.25 \ m/sec$$
2. $$1.05 \ m/sec$$
3. $$1.38 \ m/sec$$
4. $$1.63 \ m/sec$$

Answer: (c) $$1.38 \ m/sec$$

Solution: Given, length of the bridge = $$250 \ meter$$
time taken by the man to cross the bridge $$= 3 \times 60 = 180 \ seconds$$, then $$speed = \frac{distance \ covered}{time \ taken}$$ $$= \frac{250}{180} = 1.38 \ m/sec$$

1. A car goes from city A to city B at the speed of $$75 \ km/hr$$ and returns from city B to A. If the average speed of the car during the whole journey is $$65 \ km/hr$$, then find the speed of the car returns from city B to city A?

1. $$57.35 \ km/hr$$
2. $$56.25 \ km/hr$$
3. $$46.25 \ km/hr$$
4. $$58.62 \ km/hr$$

Answer: (a) $$57.35 \ km/hr$$

Solution: Given, speed of the car from city A to B $$(s_1) = 75 \ km/hr$$
Average speed of the car = $$65 \ km/hr$$
Let the distance between city A and city B = $$1 \ km$$, then $$Average \ speed = \frac{distance \ covered}{time \ taken}$$ $$Average \ speed = \frac{d_1 + d_2}{\frac{d_1}{s_1} + \frac{d_2}{s_2}}$$ $$65 = \frac{1 + 1}{\frac{1}{75} + \frac{1}{s_2}}$$ $$65 = \frac{2 \times 75 \times s_2}{(s_2 + 75)}$$ $$65 \ s_2 + 4875 = 150 \ s_2$$ $$s_2 = \frac{4875}{85} = 57.35 \ km/hr$$

1. A $$125 \ meter$$ long train passes a bridge at the speed of $$65 \ km/hr$$ in $$10 \ seconds$$, then find the length of the bridge?

1. $$56.5 \ meter$$
2. $$55.5 \ meter$$
3. $$58.5 \ meter$$
4. $$54.5 \ meter$$

Answer: (b) $$55.5 \ meter$$

Solution: Given, length of the train = $$125 \ meter$$
speed of the train = $$65 \ km/hr$$ = $$65 \times \frac{5}{18} = 18.05 \ m/sec$$
time taken by the train to cross the bridge = $$10 \ seconds$$

distance covered by the train in $$10 \ seconds$$ with the speed of $$18.05 \ m/sec$$ = $$18.05 \times 10$$ = $$180.5 \ meter$$, then length of the bridge $$= 180.5 - length \ of \ the \ train$$ $$= 180.5 - 125 = 55.5 \ meter$$

1. A train crosses a pole in $$8 \ seconds$$ with the speed of $$150 \ km/hr$$, if the length of the pole is not considered, then find the length of the train?

1. $$333.36 \ meter$$
2. $$320.25 \ meter$$
3. $$350.36 \ meter$$
4. $$325.45 \ meter$$

Answer: (a) $$333.36 \ meter$$

Solution: Given, speed of the train $$(s_m) = 150 \ km/hr$$ = $$150 \times \frac{5}{18}$$ = $$41.67 \ m/sec$$
time taken by the train to cross the pole = $$8 \ seconds$$, then $$time \ taken = \frac{l_m}{s_m}$$ $$8 = \frac{l_m}{41.67}$$ $$l_m = 333.36 \ meter$$

1. A $$1000 \ meter$$ long train crossed a $$250 \ meter$$ long bridge with the speed of $$200 \ km/hr$$. If length of the bridge is considered then find the time taken by the train to cross the bridge?

1. $$20.50 \ seconds$$
2. $$24.25 \ seconds$$
3. $$22.49 \ seconds$$
4. $$25.62 \ seconds$$

Answer: (c) $$22.49 \ seconds$$

Solution: Given, length of the train $$(l_m) = 1000 / meter$$
length of the bridge $$(l_s) = 250 \ meter$$
speed of the train $$(s_m) = 200 \ km/hr$$ = $$200 \times \frac{5}{18} = 55.56 \ m/sec$$, then $$time \ taken = \frac{l_m + l_s}{s_m}$$ $$= \frac{1000 + 250}{55.56} = 22.49 \ seconds$$