Time & Distance Questions and Answers

Q: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]\[ 54 \text{ kmph} = 15 \text{ m/s} \]\[ t = \frac{540 + 180}{15} = \frac{720}{15} = 48 \text{ sec} \]

Q: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?

Crossing the bridge covers the train plus the bridge.\[ v = \frac{100 + 300}{45} = \frac{400}{45} = 8.89 \text{ m/s} \]\[ 8.89 \times \frac{18}{5} = 32 \text{ kmph} \]

Q: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

\[ v_{2} = \frac{400}{4} = 100 \text{ km/hr} \]The speeds are in the ratio \( 7 : 8 \), so\[ v_{1} = 100 \times \frac{7}{8} = 87.5 \text{ km/hr} \]The first train is the slower of the two, so its speed must fall below 100 - which rules out one option without any calculation.

Q: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.

Each half of the distance is \( \tfrac{d}{2} \).\[ \frac{d/2}{30} + \frac{d/2}{25} = 11 \]\[ \frac{d}{60} + \frac{d}{50} = \frac{5d + 6d}{300} = \frac{11d}{300} \]\[ \frac{11d}{300} = 11 \quad\Longrightarrow\quad d = 300 \text{ km} \]Equivalently, the average speed is the harmonic mean \( \tfrac{2 \times 30 \times 25}{55} = 27.27 \) kmph, and \( 27.27 \times 11 = 300 \).

Q: One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?

\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]Put both speeds in the same units.\[ 45 \text{ kmph} = 45 \times \frac{5}{18} = 12.5 \text{ m/s} \]\[ 12.5 : 10 = 5 : 4 \]Comparing 45 with 10 directly would give the meaningless 9 : 2 - the third option.

Q: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?

The first train leaves five hours earlier, so it is\[ 30 \times 5 = 150 \text{ km} \]ahead at 2 p.m. The gap closes at \( 40 - 30 = 10 \) kmph:\[ t = \frac{150}{10} = 15 \text{ hours} \]\[ \text{distance from Delhi} = 40 \times 15 = 600 \text{ km} \]Checking with the first train: \( 30 \times 20 = 600 \) km in the twenty hours since 9 a.m.

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121.

Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?

A.10 min
B.11 min
C.12 min
D.13 min

Answer: C

In one hour of clock time the train covers 36 km instead of 45, losing 9 km of travel.

\[ t = \frac{9}{45} \text{ h} = \frac{1}{5} \text{ h} = 12 \text{ minutes} \]

The lost distance is timed at the running speed of 45 kmph, since that is the speed it would have been covered at.

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122.

A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?

A.20 kmph
B.24 kmph
C.50 kmph
D.35 kmph

Answer: B

Equal distances each way call for the harmonic mean, not the arithmetic one.

\[ \bar{v} = \frac{2 \times 20 \times 30}{20 + 30} = \frac{1200}{50} = 24 \text{ kmph} \]

The arithmetic mean of 25 kmph is too high, because more time is spent on the slower outward leg.

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123.

A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?

A.40 sec
B.44 sec
C.48 sec
D.52 sec

Answer: C

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

\[ 54 \text{ kmph} = 15 \text{ m/s} \]

\[ t = \frac{540 + 180}{15} = \frac{720}{15} = 48 \text{ sec} \]

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124.

A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?

A.32 kmph
B.36 kmph
C.40 kmph
D.48 kmph

Answer: A

Crossing the bridge covers the train plus the bridge.

\[ v = \frac{100 + 300}{45} = \frac{400}{45} = 8.89 \text{ m/s} \]

\[ 8.89 \times \frac{18}{5} = 32 \text{ kmph} \]

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125.

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

A.70 km/hr
B.75 km/hr
C.84 km/hr
D.87.5 km/hr

Answer: D

\[ v_{2} = \frac{400}{4} = 100 \text{ km/hr} \]

The speeds are in the ratio \( 7 : 8 \), so

\[ v_{1} = 100 \times \frac{7}{8} = 87.5 \text{ km/hr} \]

The first train is the slower of the two, so its speed must fall below 100 - which rules out one option without any calculation.

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126.

Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.

A.240 km
B.280 km
C.260 km
D.300 km

Answer: D

Each half of the distance is \( \tfrac{d}{2} \).

\[ \frac{d/2}{30} + \frac{d/2}{25} = 11 \]

\[ \frac{d}{60} + \frac{d}{50} = \frac{5d + 6d}{300} = \frac{11d}{300} \]

\[ \frac{11d}{300} = 11 \quad\Longrightarrow\quad d = 300 \text{ km} \]

Equivalently, the average speed is the harmonic mean \( \tfrac{2 \times 30 \times 25}{55} = 27.27 \) kmph, and \( 27.27 \times 11 = 300 \).

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127.

Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?

A.25 min
B.26 min
C.27 min
D.28 min

Answer: D

Speed and time are inversely proportional over a fixed distance, so walking at \( \tfrac{7}{6} \) of his rate takes \( \tfrac{6}{7} \) of the time.

\[ t - \frac{6}{7}t = \frac{1}{7}t = 4 \text{ min} \]

\[ t = 28 \text{ minutes} \]

Checking: the faster walk takes 24 minutes, exactly 4 less.

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128.

A car is running at a speed of 90 kmph. What distance will it cover in 15 second?

A.100 m
B.255 m
C.375 m
D.Cannot be determined

Answer: C

Convert to metres per second with the factor \( \tfrac{5}{18} \).

\[ 90 \text{ kmph} = 90 \times \frac{5}{18} = 25 \text{ m/s} \]

\[ \text{distance} = 25 \times 15 = 375 \text{ m} \]

The data are complete, so "cannot be determined" is a trap. Working in kilometres and hours would need \( 15 \) s \( = \tfrac{1}{240} \) h, giving 0.375 km - the same answer.

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129.

One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?

A.5:4
B.4:5
C.9:2
D.2:9

Answer: A

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

Put both speeds in the same units.

\[ 45 \text{ kmph} = 45 \times \frac{5}{18} = 12.5 \text{ m/s} \]

\[ 12.5 : 10 = 5 : 4 \]

Comparing 45 with 10 directly would give the meaningless 9 : 2 - the third option.

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130.

A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?

A.300 km
B.400 km
C.600 km
D.None

Answer: C

The first train leaves five hours earlier, so it is

\[ 30 \times 5 = 150 \text{ km} \]

ahead at 2 p.m. The gap closes at \( 40 - 30 = 10 \) kmph:

\[ t = \frac{150}{10} = 15 \text{ hours} \]

\[ \text{distance from Delhi} = 40 \times 15 = 600 \text{ km} \]

Checking with the first train: \( 30 \times 20 = 600 \) km in the twenty hours since 9 a.m.

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