Time & Distance Questions and Answers

Q: Ajay and Vijay travel from A to B at 17 km/hr and 19 km/hr, respectively. A is 72km away from B. Vijay reaches B first and returns immediately and meets Ajay at C. Find B to C distance?

Vijay reaches B first:\[ t = \frac{72}{19} \text{ h} \]By then Ajay has covered\[ 17 \times \frac{72}{19} = \frac{1224}{19} = 64.42 \text{ km} \]so they are \( 72 - 64.42 = 7.58 \) km apart and now approaching each other at \( 17 + 19 = 36 \) km/hr:\[ t' = \frac{7.58}{36} = 0.2105 \text{ h} \]\[ BC = 19 \times 0.2105 = 4 \text{ km} \]After the turn the two are closing, so the speeds add; before it they were separating, so only Ajay's progress mattered.

Q: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]\[ 60 \text{ kmph} = \frac{50}{3} \text{ m/s} \]\[ t = \frac{110 + 170}{50/3} = \frac{280 \times 3}{50} = 16.8 \text{ sec} \]

Q: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]\[ 72 \text{ kmph} = 20 \text{ m/s} \]A man is a point, so only the train's own length is covered:\[ t = \frac{170}{20} = 8.5 = 8\tfrac{1}{2} \text{ sec} \]

Q: What distance will be covered by a bus moving at 72 kmph in 30 seconds?

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]\[ 72 \text{ kmph} = 20 \text{ m/s} \]\[ d = 20 \times 30 = 600 \text{ m} \]

Q: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?

Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]\[ \text{relative speed} = 54 + 72 = 126 \text{ kmph} = 35 \text{ m/s} \]To meet, only the 100 m gap between them has to close:\[ t = \frac{100}{35} = \frac{20}{7} \text{ sec} \]Their lengths play no part until they begin to pass each other.

Q: The distance between Delhi and Mathura is 110 km. A starts from Delhi at 7 a.m. with a speed of 20 kmph towards Mathura, and B starts from Mathura at 8 a.m. with a speed of 25 kmph towards Delhi. When will they meet?

A has a one-hour head start:\[ 20 \times 1 = 20 \text{ km covered by 8 a.m.} \]\[ \text{gap remaining} = 110 - 20 = 90 \text{ km} \]They approach at \( 20 + 25 = 45 \) kmph:\[ t = \frac{90}{45} = 2 \text{ hours} \]So they meet at 10 a.m.

Q: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?

Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]\[ \text{relative speed} = 50 + 70 = 120 \text{ kmph} = \frac{100}{3} \text{ m/s} \]\[ t = \frac{150 + 100}{100/3} = \frac{250 \times 3}{100} = 7.5 = 7\tfrac{1}{2} \text{ sec} \]

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101.

A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?

A.47.5
B.50
C.45
D.40

Answer: D

Average speed is total distance over total time, which for two equal legs is the harmonic mean, not the arithmetic one:

\[ \bar{v} = \frac{2v_{1}v_{2}}{v_{1} + v_{2}} \]

\[ \bar{v} = \frac{2 \times 30 \times 60}{30 + 60} = \frac{3600}{90} = 40 \text{ kmph} \]

The arithmetic mean of 45 kmph is the trap; the return trip at double the speed takes half the time, so the slow outward leg dominates.

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102.

Ajay and Vijay travel from A to B at 17 km/hr and 19 km/hr, respectively. A is 72km away from B. Vijay reaches B first and returns immediately and meets Ajay at C. Find B to C distance?

A.10 km
B.4 km
C.15 km
D.36 km

Answer: B

Vijay reaches B first:

\[ t = \frac{72}{19} \text{ h} \]

By then Ajay has covered

\[ 17 \times \frac{72}{19} = \frac{1224}{19} = 64.42 \text{ km} \]

so they are \( 72 - 64.42 = 7.58 \) km apart and now approaching each other at \( 17 + 19 = 36 \) km/hr:

\[ t' = \frac{7.58}{36} = 0.2105 \text{ h} \]

\[ BC = 19 \times 0.2105 = 4 \text{ km} \]

After the turn the two are closing, so the speeds add; before it they were separating, so only Ajay's progress mattered.

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103.

How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?

A.1.68 sec
B.15 sec
C.16 sec
D.16.8 sec

Answer: D

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]

\[ 60 \text{ kmph} = \frac{50}{3} \text{ m/s} \]

\[ t = \frac{110 + 170}{50/3} = \frac{280 \times 3}{50} = 16.8 \text{ sec} \]

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104.

A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?

A.10 ½ sec
B.9 ½ sec
C.8 ¾ sec
D.8 ½ sec

Answer: D

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]

\[ 72 \text{ kmph} = 20 \text{ m/s} \]

A man is a point, so only the train's own length is covered:

\[ t = \frac{170}{20} = 8.5 = 8\tfrac{1}{2} \text{ sec} \]

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105.

What distance will be covered by a bus moving at 72 kmph in 30 seconds?

A.250 m
B.600 m
C.750 m
D.400 m

Answer: B

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]

\[ 72 \text{ kmph} = 20 \text{ m/s} \]

\[ d = 20 \times 30 = 600 \text{ m} \]

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106.

Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?

A.10/7 sec
B.12/7 sec
C.20/7 sec
D.17/7 sec

Answer: C

Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]

\[ \text{relative speed} = 54 + 72 = 126 \text{ kmph} = 35 \text{ m/s} \]

To meet, only the 100 m gap between them has to close:

\[ t = \frac{100}{35} = \frac{20}{7} \text{ sec} \]

Their lengths play no part until they begin to pass each other.

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107.

The distance between Delhi and Mathura is 110 km. A starts from Delhi at 7 a.m. with a speed of 20 kmph towards Mathura, and B starts from Mathura at 8 a.m. with a speed of 25 kmph towards Delhi. When will they meet?

A.10.30 a.m.
B.10.00 a.m.
C.9.30 a.m.
D.9.00 a.m.

Answer: B

A has a one-hour head start:

\[ 20 \times 1 = 20 \text{ km covered by 8 a.m.} \]

\[ \text{gap remaining} = 110 - 20 = 90 \text{ km} \]

They approach at \( 20 + 25 = 45 \) kmph:

\[ t = \frac{90}{45} = 2 \text{ hours} \]

So they meet at 10 a.m.

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108.

Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?

A.3 sec
B.4 ½ sec
C.5 sec
D.7 ½ sec

Answer: D

Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]

\[ \text{relative speed} = 50 + 70 = 120 \text{ kmph} = \frac{100}{3} \text{ m/s} \]

\[ t = \frac{150 + 100}{100/3} = \frac{250 \times 3}{100} = 7.5 = 7\tfrac{1}{2} \text{ sec} \]

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109.

Rohit drives from his home at a speed of 30 km/hr and reaches his bank 20 minutes late. Then the next day he increases his speed by 15 km/hr but still he is late by 8 minutes. How far is his bank from his home?

A.18 km
B.35 km
C.20 km
D.27 km

Answer: A

Both journeys cover the same distance and both are late, so the difference in lateness is the difference in travel time.

\[ \frac{D}{30} - \frac{D}{45} = \frac{20 - 8}{60} = 0.2 \text{ h} \]

\[ D\left(\frac{3 - 2}{90}\right) = 0.2 \quad\Longrightarrow\quad \frac{D}{90} = 0.2 \]

\[ D = 18 \text{ km} \]

The scheduled arrival time never has to be found - only the 12-minute gap between the two lateness figures matters.

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110.

Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?

A.10 hours
B.13 hours
C.14 hours
D.12 hours

Answer: A

Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.

x + y = 7 --- (1) ; 2x = 4 --- (2)

solving both the equations, we get y = 5

So, time taken to cover both ways by cycle = 2y hours = 10 hours.

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