# Time Speed and Distance 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. If a $$250 \ m$$ long train crossed a $$75 \ m$$ long platform with the speed of $$60 \ km/hr$$, then find the time taken by the train to cross the platform?

1. $$22.5 \ seconds$$
2. $$19.5 \ seconds$$
3. $$20.5 \ seconds$$
4. $$25.5 \ seconds$$

Answer: (b) $$19.5 \ seconds$$

Solution: Given, length of the train $$(l_m) = 250 \ m$$
length of the platform $$(l_s) = 75 \ m$$
speed of the train $$(s_m) = 60 \ km/hr = 60 \times \frac{5}{18} = \frac{50}{3} \ m/sec$$, then $$time \ taken \ (T) = \frac{l_m + l_s}{s_m}$$ $$= \frac{250 + 75}{\frac{50}{3}}$$ $$= \frac{325 \times 3}{50} = 19.5 \ sec.$$

1. If a $$380 \ m$$ long train crossed a $$125 \ m$$ long platform in $$12 \ sec$$, then find the speed of the train?

1. $$42.083 \ m/sec$$
2. $$40.205 \ m/sec$$
3. $$45.525 \ m/sec$$
4. $$38.325 \ m/sec$$

Answer: (a) $$42.083 \ m/sec$$

Solution: Given, length of the train $$(l_m) = 380 \ m$$
length of the platform $$(l_s) = 125 \ m$$
time taken by the train to cross the platform $$(T) = 12 \ seconds$$, then $$Time \ taken \ (T) = \frac{l_m + l_s}{s_m}$$ $$12 = \frac{380 + 125}{s_m}$$ $$s_m = \frac{505}{12} = 42.083 \ m/sec$$

1. If a car covered $$280 \ km$$ in $$4 \ hours$$ then find the speed of the car?

1. $$68 \ km/hr$$
2. $$75 \ km/hr$$
3. $$70 \ km/hr$$
4. $$72 \ km/hr$$

Answer: (c) $$70 \ km/hr$$

Solution: Given, distance covered by the car = $$280 \ km$$, time taken = $$4 \ hours$$, then the speed of the car $$speed = \frac{distance \ covered}{time \ taken}$$ $$speed = \frac{280}{4} = 70 \ km/hr$$

1. If a train crossed a $$160 \ m$$ long platform in $$2.5 \ seconds$$, with the speed of $$130 \ m/sec$$, then find the length of the train?

1. $$168 \ meters$$
2. $$175 \ meters$$
3. $$155 \ meters$$
4. $$165 \ meters$$

Answer: (d) $$165 \ meters$$

Solution: Given, length of the platform $$(l_s) = 160 \ meters$$
speed of the train $$(s_m) = 130 \ m/sec$$
time taken $$(T) = 2.5 \ seconds$$, then $$time \ taken \ (T) = \frac{l_m + l_s}{s_m}$$ $$2.5 = \frac{l_m + 160}{130}$$ $$l_m = 325 - 160 = 165 \ meters$$

1. If a $$425 \ meters$$ long train crossed a platform in $$3.6 \ seconds$$ with the speed of $$160 \ m/sec$$, then find the length of the platform?

1. $$157 \ meters$$
2. $$151 \ meters$$
3. $$152 \ meters$$
4. $$156 \ meters$$

Answer: (b) $$151 \ meters$$

Solution: Given, length of the train $$(l_m) = 425 \ meters$$
speed of the train $$(T) = 3.6 \ seconds$$, then $$time \ taken \ (T) = \frac{l_m + l_s}{s_m}$$ $$3.6 = \frac{425 + l_s}{160}$$ $$l_s = 576 - 425 = 151 \ meters$$

1. A train is moving at the speed of $$280 \ km/hr$$ and one another train also moving parallel to the first train in the same direction with the speed of $$230 \ km/hr$$, then find the relative speed of the trains?

1. $$50 \ km/hr$$
2. $$56 \ km/hr$$
3. $$52 \ km/hr$$
4. $$58 \ km/hr$$

Answer: (a) $$50 \ km/hr$$

Solution: Given, speed of the first train $$(s_1) = 280 \ km/hr$$
speed of the second train $$(s_2) = 230 \ km/hr$$, then $$Relative \ speed = s_1 - s_2$$ $$= 280 - 230 = 50 \ km/hr$$

1. If the speed of a man is $$45 \ m/sec$$, then find the speed of the man in $$km/hr$$?

1. $$158 \ km/hr$$
2. $$162 \ km/hr$$
3. $$165 \ km/hr$$
4. $$156 \ km/hr$$

Answer: (b) $$162 \ km/hr$$

Solution: speed of the man = $$45 \ m/sec$$, then $$= 45 \times \frac{18}{5} = 162 \ km/hr$$

1. If a train covered first $$10 \ km$$ at the speed of $$80 \ km/hr$$ and second $$20 \ km$$ at the speed of $$100 \ km/hr$$, then find the average speed of the train?

1. $$98.5 \ km/hr$$
2. $$93.2 \ km/hr$$
3. $$92.3 \ km/hr$$
4. $$94.6 \ km/hr$$

Answer: (c) $$92.3 \ km/hr$$

Solution: $$Average \ speed = \frac{distance \ covered}{time \ taken}$$ $$= \frac{10 + 20}{\frac{10}{80} + \frac{20}{100}}$$ $$= \frac{30 \times 400}{50 + 80}$$ $$= \frac{12000}{130} = 92.3 \ km/hr$$

1. If a train travels from A to B at the speed of $$x_1 \ km/hr$$ and travels from B to A at the speed of $$x_2 \ km/hr$$, then find the average speed of the train?

1. $$\frac{x_1 + x_2}{2 \ x_1 \ x_2} \ km/hr$$
2. $$\frac{2 \ x_1 \ x_2}{x_1 + x_2} \ km/hr$$
3. $$\frac{x_1 - x_2}{2 \ x_1 \ x_2} \ km/hr$$
4. $$\frac{2 \ x_1 \ x_2}{x_1 - x_2} \ km/hr$$

Answer: (b) $$\frac{2 \ x_1 \ x_2}{x_1 + x_2} \ km/hr$$

Solution: Let the distance between A to B = $$d \ km$$, then $$Average \ speed = \frac{distance \ covered}{time \ taken}$$ $$= \frac{d + d}{\frac{d}{x_1} + \frac{d}{x_2}}$$ $$\frac{2d \times x_1 \ x_2}{d \ (x_2 + x_1)}$$ $$= \frac{2 \ x_1 \ x_2}{x_1 + x_2} \ km/hr$$

1. If two trains moving parallel in the opposite direction at the speed of $$2P \ km/hr$$ and $$3P \ km/hr$$ respectively. Find the relative speed of the train?

1. $$6P \ km/hr$$
2. $$5P \ km/hr$$
3. $$8P \ km/hr$$
4. $$7P \ km/hr$$

Answer: (b) $$5P \ km/hr$$

Solution: Given, speed of the first train $$(s_1) = 2P \ km/hr$$
speed of the second train $$(s_2) = 3P \ km/hr$$, then $$Relative \ speed = s_1 + s_2$$ $$= 2P + 3P = 5P \ km/hr$$