# Time Speed and Distance Quantitative 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 $$450 \ meter$$ and $$550 \ meter$$ long trains moving in the same direction at the speed of $$85 \ km/hr$$ and $$75 \ km/hr$$ respectively. Find the time taken by the faster train to cross the slower train?

1. $$250 \ seconds$$
2. $$360 \ seconds$$
3. $$380 \ seconds$$
4. $$320 \ seconds$$

Answer: (b) $$360 \ seconds$$

Solution: Given, length of the first train $$(l_1) = 450 \ meter$$

length of the second train $$(l_2) = 550 \ meter$$

speed of the first train $$(s_1) = 85 \ km/hr = 85 \times \frac{5}{18} \ m/sec$$

speed of the second train $$(s_2) = 75 \ km/hr = 75 \times \frac{5}{18} \ m/sec$$, then $$Time \ taken \ (T) = \frac{l_1 + l_2}{s_1 - s_2}$$ $$= \frac{450 + 550}{\frac{5}{18} \ (85 - 75)}$$ $$= \frac{1000 \times 18}{10 \times 5}$$ $$= \frac{18000}{50} = 360 \ sec$$

1. Two $$700 \ meter$$ and $$800 \ meter$$ long trains, moving in the same direction. Faster train takes $$200 \ seconds$$ to cross the slower train. If speed of the first train is $$70 \ km/hr$$, then find the speed of the second train?

1. $$42.98 \ km/hr$$
2. $$40.36 \ km/hr$$
3. $$45.62 \ km/hr$$
4. $$46.25 \ km/hr$$

Answer: (a) $$42.98 \ km/hr$$

Solution: Given, length of the first train $$(l_1) = 700 \ meter$$

length of the second train $$(l_2) = 800 \ meter$$

speed of the first train $$(s_1) = 70 \ km/hr = 70 \times \frac{5}{18} \ m/sec$$

time taken by the faster train to cross the slower one = $$200 \ seconds$$, then $$Time \ taken \ (T) = \frac{l_1 + l_2}{s_1 - s_2}$$ $$200 = \frac{700 + 800}{70 \times \frac{5}{18} - s_2}$$ $$200 = \frac{1500 \times 18}{70 \times 5 - 18 \ s_2}$$ $$200 = \frac{27000}{350 - 18 \ s_2}$$ $$70000 - 3600 \ s_2 = 27000$$ $$3600 \ s_2 = 43000$$ $$s_2 = \frac{43000}{3600} = 11.94 \ m/sec$$ $$= 11.94 \times \frac{18}{5} \ km/hr$$ $$= 42.98 \ km/hr$$

1. The $$250 \ meter$$ long train x is moving from station A to station B, at the speed of $$40 \ km/hr$$ and the $$300 \ meter$$ long train y is moving from station B to station A. If both the trains taken $$25 \ seconds$$ to pass each other, then find the speed of the train y moving from station B to A?

1. $$9.4 \ m/sec$$
2. $$11.6 \ m/sec$$
3. $$10.89 \ m/sec$$
4. $$12.59 \ m/sec$$

Answer: (c) $$10.89 \ m/sec$$

Solution: Given, length of the train x $$(l_1) = 250 \ meter$$

length of the train y $$(l_2) = 300 \ meter$$

speed of the train x = $$(s_1) = 40 \ km/hr = 40 \times \frac{5}{18} \ m/sec$$

time taken by the trains to pass each other $$(T) = 25 \ seconds$$, then $$Time \ taken \ (T) = \frac{l_1 + l_2}{s_1 + s_2}$$ $$25 = \frac{250 + 300}{40 \times \frac{5}{18} + s_2}$$ $$25 = \frac{550 \times 18}{200 + 18s_2}$$ $$5000 + 450 \ s_2 = 9900$$ $$450 \ s_2 = 4900$$ $$s_2 = 10.89 \ m/sec$$

1. Two metro trains $$150 \ meter$$ and $$160 \ meter$$ long, moving in the opposite direction with the speed of $$45 \ m/sec$$ and $$50 \ m/sec$$ respectively. Find how much time the metro trains will take to pass each other?

1. $$3.42 \ seconds$$
2. $$5.25 \ seconds$$
3. $$4.36 \ seconds$$
4. $$3.26 \ seconds$$

Answer: (d) $$3.26 \ seconds$$

Solution: Given, length of the first metro train $$(l_1) = 150 \ meter$$

length of the second metro train $$(l_2) = 160 \ meter$$

speed of the first metro train $$(s_1) = 45 \ m/sec$$

speed of the second metro train $$(s_2) = 50 \ m/sec$$, then $$Time \ taken \ (T) = \frac{l_1 + l_2}{s_1 + s_2}$$ $$= \frac{150 + 160}{45 + 50}$$ $$= \frac{310}{95} = 3.26 \ sec$$

1. Two buses $$60 \ meter$$ and $$80 \ meter$$ long, moving in the same direction with the speed of $$x \ m/sec$$ and $$200 \ m/sec$$ respectively. If faster bus will pass the slower one in $$5 \ seconds$$, then find the value of $$x$$?

1. $$225 \ m/sec$$
2. $$228 \ m/sec$$
3. $$232 \ m/sec$$
4. $$230 \ m/sec$$

Answer: (b) $$228 \ m/sec$$

Solution: Given, length of the first bus $$(l_1) = 60 \ meter$$

length of the second bus $$(l_2) = 80 \ meter$$

speed of the first bus $$(s_1) = x \ m/sec$$

speed of the second bus $$(s_2) = 200 \ m/sec$$

time taken by the faster bus to cross the slower one $$(T) = 5 \ seconds$$, then $$Time \ taken \ (T) = \frac{l_1 + l_2}{s_1 - s_2}$$ $$5 = \frac{60 + 80}{x - 200}$$ $$5 \ x - 1000 = 140$$ $$x = \frac{1140}{5} = 228 \ m/sec$$

1. A man covered half of his distance with the speed of $$120 \ m/sec$$ and second half covered with the speed of $$140 \ m/sec$$. Find the average speed of the man during the whole journey?

1. $$126.25 \ m/sec$$
2. $$128.05 \ m/sec$$
3. $$129.23 \ m/sec$$
4. $$127.63 \ m/sec$$

Answer: (c) $$129.23 \ m/sec$$

Solution: Given, speed of the man during one half = $$120 \ m/sec$$

speed of the man during second half = $$140 \ m/sec$$

Let total distance = $$1 \ meter$$, then $$Average \ speed = \frac{distance \ covered}{time \ taken}$$ $$= \frac{d_1 + d_2}{\frac{d_1}{s_1} + \frac{d_2}{s_2}}$$ $$= \frac{0.5 + 0.5}{\frac{0.5}{120} + \frac{0.5}{140}}$$ $$= \frac{1 \times 240 \times 280}{280 + 240}$$ $$= \frac{67200}{520} = 129.23 \ m/sec$$

1. Two cars moving in the same direction with the speed of $$180 \ m/sec$$ and $$160 \ m/sec$$ respectively. Find the relative speed of the cars?

1. $$75 \ km/hr$$
2. $$70 \ km/hr$$
3. $$76 \ km/hr$$
4. $$72 \ km/hr$$

Answer: (d) $$72 \ km/hr$$

Solution: Given, speed of the first car $$(s_1) = 180 \ m/sec$$

speed of the second car $$(s_2) = 160 \ m/sec$$, then $$Relative \ speed = s_1 - s_2$$ $$= 180 - 160 = 20 \ m/sec$$ $$= 20 \times \frac{18}{5} = 72 \ km/hr$$

1. A car covered $$0.8 \ \%$$ distance of the journey at the speed of $$60 \ m/sec$$ and covered $$0.2 \ \%$$ of the journey with the speed of $$80 \ m/sec$$, then find the average speed of the car?

1. $$66.25 \ m/sec$$
2. $$65.35 \ m/sec$$
3. $$63.15 \ m/sec$$
4. $$64.25 \ m/sec$$

Answer: (c) $$63.15 \ m/sec$$

Solution: Given, speed of the car during $$0.8 \ \%$$ of distance = $$60 \ m/sec$$

speed of the car remaining $$0.2 \ \%$$ of distance = $$80 \ m/sec$$

Let total distance = $$1 \ meter$$, then $$Average \ speed = \frac{distance \ covered}{time \ taken}$$ $$= \frac{d_1 + d_2}{\frac{d_1}{s_1} + \frac{d_2}{s_2}}$$ $$= \frac{0.8 + 0.2}{\frac{0.8}{60} + \frac{0.2}{80}}$$ $$= \frac{1}{\frac{1}{75} + \frac{1}{400}}$$ $$= \frac{1 \times 30000}{400 + 75}$$ $$= \frac{30000}{475}$$ $$Average \ speed = 63.15 \ m/sec$$

1. Two cars, moving in the opposite direction with the speed of $$25 \ km/hr$$ and $$35 \ km/hr$$ respectively. Find the relative speed of the cars?

1. $$65 \ km/hr$$
2. $$60 \ km/hr$$
3. $$62 \ km/hr$$
4. $$58 \ km/hr$$

Answer: (b) $$60 \ km/hr$$

Solution: Given, speed of the first car $$(s_1) = 25 \ km/hr$$

speed of the second car $$(s_2) = 35 \ km/hr$$, then $$Relative \ speed = s_1 + s_2$$ $$= 25 + 35 = 60 \ km/hr$$

1. If a $$600 \ meter$$ long train crossed a $$300 \ meter$$ platform with the speed of $$200 \ m/sec$$. If the length of the platform is considered then find the time taken by the train to cross the platform?

1. $$4.5 \ seconds$$
2. $$4.2 \ seconds$$
3. $$5.5 \ seconds$$
4. $$5.2 \ seconds$$

Answer: (a) $$4.5 \ seconds$$

Solution: Given, length of the train $$(l_m) = 600 \ meter$$

length of the platform $$(l_s) = 300 \ meter$$

speed of the train $$(s_m) = 200 \ m/sec$$, then $$Time \ taken = \frac{l_m + l_s}{s_m}$$ $$= \frac{600 + 300}{200} = 4.5 \ sec$$