MATHEMATICS > Time and Distance
1) Train A crosses a stationary train B in 35 seconds and a pole in 14 seconds with the same speed. The length of train A is 280 meters. What is the length of the stationary train B
A) 360 metersB) 480 meters
C) 420 metersD) None of the above
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Answer : 420 meters

\begin{aligned} \frac{280+L}{35}=\frac{280}{14}\\ 280+L=\left(\frac{280}{14*35}\right)\\ 280+L=700\\ L=420\\ \end{aligned}

2) A train, when it moves at an average speed of 40 kmph, reaches its destination on time, When its average speed becomes 35 kmph, it reaches its destination 15 minutes late. Find the length of the journey
A) 70 kmB) 60 km
C) 80 kmD) None of the above
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Answer : 70 km

\begin{aligned} \text{Timing differences is = 15 min}\\ = \frac{1}{4} hr\\ \text{Length of journey bex km}\\ \text{Therfore,}\frac{x}{35} -\frac{x}{40} = \frac{1}{4}\\ \text{8x- 7x= 70}\\ x = 70 km\\ \end{aligned}

3) A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel 1 minute, then the length of the tunnel (in meters) is
A) 130 mB) 360 m
C) 500 mD) 540 m
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Answer : 500 m

\begin{aligned} \text{S1 = 78 }\frac{km}{hr}\\ \text{L = 800 m}\\ \text{T = 1 min}\\ \text{Converting }\frac{km}{hr}\text{ to }\frac{m}{sec}\text{ using }\frac{5}{18}\\ \text{S1 = }\left(\frac{78 * 5 }{ 8}\right) \frac{m}{sec} = \left(\frac{65}{3}\right)\frac{m}{sec}\\ \text{Converting Time from min to sec}\\ \text{T = 1 min =60 sec}\\ \text{Let length of the tunnel beymetres}\\ \text{Therfore, }\left(\frac{800 + y}{60}\right)=\frac{65}{3}\\ \text{3 ( 800 + y ) = 3900}\\ \text{x = 500}\\ \end{aligned}

4) A train 110 metres long is running with a speed of 60 kmph. In what time will it pass the man who is running at 0 kmph in the direction opposite to that in which the train going
A) 5 secB) 6 sec
C) 7 secD) 10 sec
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Answer : 6 sec

\begin{aligned}\\ \text{Let Distance D = 110 m}\\ \text{Relative speed of train and man = 60 + 6}\\\text{ = 66 kmph (Since both are in moving in opposite direction)}\\ \text{= }\frac{66 * 10}{36}\text{ mps }\\ \text{= }\frac{110}{6}\text{ mps}\\ Time = \frac{distance}{speed}\\ = \frac{110}{\left(\frac{110}{6}\right)}\\ = 6 s \end{aligned}

5) Find the length of the platform which a train 400 m long, travelling at 45 km/hour, can cross in 40 seconds
A) 100 mB) 110 m
C) 120 mD) 150 m
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Answer : 100 m

\begin{aligned}\\ \text{Length of train L1 = 400 m}\\ \text{Time T = 45 }\frac{km}{hr}\\ \frac{45*5}{18}=\frac{\left( L + 400 \right)}{40}\\ \frac{ 45 * 5 * 40}{18}=L+400\\ \text{500 - 400 = L}\\ \text{L = 100} \end{aligned}

6) A car covers a certain distance at 90 km/hour speed and returns back to the starting point at 60 km/hour speed. Find its average speed for the entire journey
A) 70 km/hourB) 72 km/hour
C) 75 km/hourD) 80 km/hour
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Answer : 72 km/hour

\begin{aligned}\\ \text{Average speed of the car}=\frac{2xy}{(x+y)} \frac{km}{hr}\\ =\frac{2*90*60}{(90+60)}\\ =\frac{2*5400}{150}\\ =36*2\\ Avg.Speed=72\\ \end{aligned}

7) A man performs 2/25 of his total journey by bus, 21/50 by car and the remaining 2 km on foot his total journey is
A) 2.5 kmB) 3 km
C) 3.5 kmD) 4 km
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Answer : 4 km

\begin{aligned}\\ \frac{2}{25}(x)+\frac{21}{50}(x)+2=x\\ \frac{(4+21)}{50}(x)+2=x\\ x-\frac{1}{2}(x)=2\\ x=4\\ \end{aligned}

8) An express train travelling at 80 km/hr overtakes a goodi trains, twice as long and going 40 km/hr on a parallel track in 54 seconds. How long will the express train take to cross station 400 m long
A) 36 secB) 45 sec
C) 27 secD) 32 sec
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Answer : 27 sec


9) An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the ssm distance in l 2/3 hours, it must travel at a speed of
A) 300 kmphB) 360 kmph
C) 600 kmphD) 720 kmph
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Answer : 720 kmph

\begin{aligned} \text {Speed S1 = 240 kmph }\\
\text {Time T1 = 5 hr }\\
\text { Time T2 = } 1 \frac{2}{3} hr \\
\text {Speed S2} = ? \\
\text { Converting to rational } \frac {3 + 2 } {3} = \frac {5}{3} \\
(?) \text {S1 * T1 = S2 * T2} \\
\text {T2 = } \frac{S1 * T1}{S2} \\
\text {Substitute above values in the above equation}\\
\text{S2 = } \frac{240 * 5 }{\frac{5}{3}} \\ = \frac{240 * 5 * 3}{5}=240 * 3 = 720
\end{aligned}


10) A car travels 70 km in one hour before some fault happens, then it travels for 120 km at 30 kmph. For the entire trip, what was the average speed
A) 33 kmphB) 36 kmph
C) 38 kmphD) 40 kmph
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Answer : 38 kmph

\begin{aligned} \text{D1=70 km}\\ \text{T1=1 hr}\\ \text{D2=120 km}\\ \text{S2=30 km/hr}\\ \text{Average speed=}\frac{2xy}{\left(x+y\right)}\\ \text{T2 = }\frac{120}{30}=4 hr\\ \text{S1=}\frac{D1}{T1}=\frac{70}{1}= 70 km/hr\\ =\frac{2*70*30}{\left(70+30\right)}\\ =\frac{2*2100}{100}=2*21=42 km/hr\\ \end{aligned}