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 $$ Relative \ speed = s_1 + s_2 $$ $$ = 2P + 3P = 5P \ km/hr $$