ICSE Board: Suggested Books     ICSE Board:  Foundation Mathematics
Class 8: Reference Books               Class 8: NTSE Preparation
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Q1. A train 150 m long is running at a uniform speed of 90 km/ hr. Find:

i) The time taken by it to cross a man standing on the platform.

Length of the Train = 150 \hspace{2pt}m

Speed of the Train = 90 \hspace{2pt}\frac{km}{hr}  

Time Taken = \frac{150}{90 \times \frac{1000}{3600}}  = 6 sec

ii) The time taken by it to cross a platform 250 m long.

Length of the Train = 150\hspace{2pt} m

Speed of the Train = 90 \hspace{2pt}\frac{km}{hr}  

Length of the platform = 250\hspace{2pt} m

Time Taken = \frac{(250 + 150)}{90 \times \frac{1000}{3600}}  = 16 sec

 

Q2. A train 280 m long is running at a uniform speed, of 63 km / hr. Find:

i) The time taken by it to cross a telephonic pole.

Length of the Train = 280\hspace{2pt} m

Speed of the Train =63 \hspace{2pt}\frac{km}{hr}  

Time Taken = \frac{280}{63 \times \frac{1000}{3600}}  = 16 sec

ii) The time taken by it to cross a bridge 210 m long.

Length of the bridge = 250 \hspace{2pt}m

Time Taken = \frac{(210 + 280)}{63 \times \frac{1000}{3600}}  = 28 sec

 

Q3. A train 180 m long passes a telegraph post in 12 seconds. Find:

i) Its speed in km/hr.

Length of the Train = 180 \hspace{2pt}m

Time taken by the Train = 12 s 

Let the speed be x \hspace{2pt}\frac{m}{s}

12 = \frac{180}{x} \hspace{5pt} or \hspace{5pt} x = 15\frac{m}{s} \hspace{5pt} or \hspace{5pt}  54 \hspace{2pt}\frac{km}{hr}  

ii) The time taken by it to pass a platform 135 meters long

Length of the Platform = 135 \hspace{2pt}m

Time Taken \frac{180+135}{15} = 21 \hspace{2pt}s 

 

Q4. With a speed of 60 km/hr, a train crosses a pole in 24 seconds. Find the length of the train.

Answer:

Let the length of the train = x \hspace{2pt}m

24 = \frac{x}{60 \times \frac{1000}{3600}}  

x = 400 \hspace{2pt}m 

 

Q5. A train 700 m long is running at 72km/hr. If it crosses a tunnel in one minute, find the length of the tunnel.

Answer:

Let the length of the train = x \hspace{2pt}m

60 = \frac{700 + x}{72 \times \frac{1000}{3600}}  

x = 500 \hspace{2pt}m 

 

Q6. A train 270 m long takes 20 seconds to cross a bridge 330 m long. Find:

Answer:

i) The speed of the train in km/hr

Let the speed be  x \hspace{2pt} \frac{m}{s}

20 = \frac{(270+330)}{x} \hspace{5pt} or  x = 30 \hspace{2pt} \frac{m}{s}  \hspace{5pt} or  \hspace{5pt} 108 \hspace{2pt} \frac{km}{hr} 

ii) Time taken by it to cross an electric pole.

Time Taken = \frac{270}{30} = 9\hspace{2pt}s 

 

Q7. A train, 225 m in length, crosses a man standing on a platform in 10 seconds and a bridge in 28 seconds. Find:

Answer:

i) The speed of the train in km/hr and

Let the speed be  x \hspace{2pt} \frac{m}{s}

10 = \frac{225}{x}   \hspace{5pt} or  \hspace{5pt}   x = 22.5 \frac{m}{s}   \hspace{5pt} or \hspace{5pt} 81 \frac{km}{hr} 

ii) The length of the bridge

Let the length of the bridge be  x \hspace{2pt}m

28 = \frac{(225+x)}{22.5} \hspace{5pt} or \hspace{5pt} x = 405 \hspace{2pt}m  

 

Q8. A train running at 54 km/hr crosses a telegraph post in 16 seconds and a platform in 40 seconds. Find

Answer:

i) The length of the train and

Let the lenght of the train  x \hspace{2pt}m

16 = \frac{x}{54 \times \frac{1000}{3600}} \hspace{5pt} or  \hspace{5pt} x = 240 \hspace{2pt}m 

ii) The length of the platform.

Let the length of the platform be  x \hspace{2pt}m

40 = \frac{240+x}{54 \times \frac{1000}{3600}} \hspace{5pt} or  \hspace{5pt} x = 360 \hspace{2pt}m 

 

Q9. Two cars are 351 km apart. They start at the same time and drive towards each other. One travels at 70 km/hr and the other travels at 65 km/hr. How much time do they take to meet each other?

Answer:

Time taken  = \frac{351 km}{(70+65) \frac{km}{hr}} = 2.6 hr \hspace{5pt} or  \hspace{5pt} 156 minutes

 

Q10. In how much time will a train 250 m long, running at 50 km/hr pass a man, running at 5 km/hr in the same direction in which the train is going?

Answer:

Time taken  = \frac{250 m}{(50-5) \times \frac{1000}{3600} \frac{m}{s}} \hspace{5pt} or  \hspace{5pt} 20 seconds 

 

Q11. In how much time will a train 180 m long, running at 66 km/hr pass a man, running at 6 km/hr in a direction opposite to that in which the train is going?

Answer:

Time taken  = \frac{180 m}{(66+6) \times \frac{1000}{3600} \frac{m}{s}}  \hspace{5pt} or  \hspace{5pt} 9 seconds 

 

Q12. A and B are two trains of lengths 250 m and 200 m respectively. They are running on parallel rails at 45 km/hr and 36 km/hr respectively in opposite directions. In how much time will they be clear of each other from the moment they meet?

Answer:

Time taken  = \frac{(250+200) m}{(45+36) \times \frac{1000}{3600} \frac{m}{s}}  \hspace{5pt} =  \hspace{5pt} 20 \hspace{2pt}seconds 

 

Q13. A and B are two trains of lengths 160 m and 140 m. They are running on parallel rails in the same direction at72km/hr and 27 km/hr respectively. In how much time will A pass B completely, from the moment they meet?

Answer:

Time taken  = \frac{(160+140) m}{(72-27) \times \frac{1000}{3600} \frac{m}{s}}  \hspace{5pt} =  \hspace{5pt} 24 \hspace{2pt}seconds 

 

Q14. A train 120 m long, travelling at 45 km/hr, overtakes another train travelling in the same direction at 36 km/hr and passes it completely in 80 seconds. Find the length of the second train.

Answer:

Let the lenght of the second train  x \hspace{2pt}m

80 = \frac{(120+x)m}{(45-36) \times \frac{1000}{3600} \frac{m}{s} }   \hspace{5pt} or  \hspace{5pt} x = 80\hspace{2pt}m  

 

Q15. The speed of a boat in still water is 8 km/hr and the speed of the stream is 2.5 km/hr- Find:

Answer:

i) The time taken by the boat to go 63 km downstream

Time taken  = \frac{63 km}{(8+2.5)  \frac{km}{hr}}  \hspace{5pt} =  \hspace{5pt} 6 \hspace{2pt}hr 

ii) The time taken by the boat to go 22km, upstream.

Time taken  = \frac{22 km}{(8-2.5)  \frac{km}{hr} } \hspace{5pt} =  \hspace{5pt} 4 \hspace{2pt}hr 

 

Q16. A stream is flowing at 3 km/hr. A boat with a speed of 10 km/hr in still water is rowed upstream for 13 hours. Find the distance rowed. How long will it take to return to the starting point?

Answer:

Speed of Stream   = 3 \hspace{5pt} \frac{km}{hr}  

Speed of boat in still water    = 10  \hspace{5pt} \frac{km}{hr}  

Time rowed upsteram  = 13 \hspace{5pt} hr 

Let the distance covered  x \hspace{5pt} km  

13 hr = \frac{x}{(10-3) \frac{km}{hr}} = 91 \hspace{5pt} km  

Let the time taken to reach back  t \hspace{5pt} hr 

Time taken = \frac{91 km}{(10+3) \frac{km}{hr}} = 7 \hspace{5pt} hr 

 

Q17. The speed of a boat in still water is 10 km/hr. It is rowed upstream for a distance of 45 km in 6 hours. Find the speed of the stream.

Answer:

Let the speed of Stream  = x \hspace{2pt} \frac{km}{hr}  

Speed of boat in still water  = 10 \hspace{2pt} \frac{km}{hr}  

Time rowed upsteram  = 6 \hspace{5pt} hr 

Distance covered  = 45 \hspace{5pt} km 

6 \hspace{2pt} hr = \frac{45 km}{(10-x)} \hspace{5pt} or \hspace{5pt} x = 2.5 \hspace{2pt}  \frac{km}{hr}  

 

Q18. A stream is flowing at 4.8 km/hr. A boat is rowed downstream for a distance of 49 km in 3.5 hours. Find the speed of the boat in still water.

Answer:

Speed of Stream  = 4.8 \hspace{2pt} \frac{km}{hr}  

Let the Speed of boat in still water  = x \hspace{2pt} \frac{km}{hr}  

Time rowed down stream  = 3 \hspace{5pt} hr 

Distance covered  = 49 \hspace{5pt} km 

3.5 \hspace{2pt} hr = \frac{49 km}{(4+4.8)} \hspace{5pt}  or \hspace{5pt}  x = 9.2 \hspace{2pt}  \frac{km}{hr}  

 

Q19. The speed of a boat in still water is 5 km/hr and the speed of the stream is 1 km/hr. The boat is rowed upstream for a certain distance and taken back to the starting point. Find the average speed for the whole journey.

Answer:

Speed of Stream  = 1 \hspace{2pt} \frac{km}{hr}  

Speed of boat in still water   = 5 \hspace{2pt} \frac{km}{hr}  

Let the distance covered upstream  = x \hspace{5pt} km 

Total time taken to cover the journey = \frac{x}{5+1} + \frac{x}{5-1} = \frac{x}{6}+\frac{x}{4} = \frac{10}{24}x \hspace{2pt} hr 

Total  distance covered  = 2x \hspace{5pt} km 

Average Speed = \frac{ total \hspace{2pt}distance}{total \hspace{2pt}time} = \frac{2x}{\frac{10}{24}x} = 4.8 \hspace{2pt}\frac{km}{hr} 

 

Q20. The speed of a boat downstream is 16 km/hr and its speed upstream is 10 km/hr. Find the speed of the boat in still water and the rate of the stream.

Answer:

Let the Speed of Stream   = y \hspace{2pt} \frac{km}{hr}  

Let the Speed of boat in still water   = x \hspace{2pt} \frac{km}{hr}  

Therefore

x+y=16 

x-y=10 

Solving for   x    and   y    we get

x=13 \frac{km}{hr}  

y=3 \frac{km}{hr}  

 

ICSE Board: Suggested Books     ICSE Board:  Foundation Mathematics
Class 8: Reference Books               Class 8: NTSE Preparation
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