ICSE Board: Suggested Books     ICSE Board:  Foundation Mathematics
Class 8: Reference Books               Class 8: NTSE Preparation
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Q1. Express the following speeds in meter/sec:

72\hspace{2pt}\frac{km}{hr} = \frac{72\times 1000  m}{3600 sec} = 20\hspace{2pt}\frac{m}{s}

117\hspace{2pt}\frac{km}{hr} = \frac{117\times 1000 m}{3600 sec} = 32.5\hspace{2pt}\frac{ m}{s}

5.4\hspace{2pt}\frac{km}{hr} = \frac{5.4\times 1000 m}{3600 sec} = 1.5\hspace{2pt}\frac{ m}{s}

 12.6\hspace{2pt}\frac{km}{hr} = \frac{12.6 \times 1000 m}{3600 sec} = 3.5\hspace{2pt}\frac{m}{s}

 

Q2. Express the following speeds in km/hr:

18\hspace{2pt}\frac{m}{s} = \frac{18 km \times 3600}{1000 hr} = 64.8\hspace{2pt}\frac{km}{hr}

2\hspace{2pt}\frac{m}{s} = \frac{2 km \times 3600}{1000 hr} = 7.2\hspace{2pt}\frac{km}{hr}

3\frac{1}{3}\hspace{2pt}\frac{m}{s} = \frac{10 km \times 3600}{3 \times 1000 hr} = 12\hspace{2pt}\frac{km}{hr}

 12.5\hspace{2pt}\frac{m}{s} = \frac{12.5 km \times 3600}{1000 hr} = 45\hspace{2pt}\frac{km}{hr}

 

Q3. An athlete covers a distance of 1200 meters in 4 min.48 sec. Find his speed in km/hr.

Answer:

Speed = \frac{1200 m}{4 min 48 sec} = \frac{1200  km \times 3600}{1000 \times 288 hr} = 15\hspace{2pt}\frac{km}{hr}  

 

Q4. Walking at the rate of 4 km/hr a man covers a certain distance in 2\frac{1}{2}  hours. How much time will be taken by the man to cover the same distance, if he cycles at 12 km/hr?

Answer:

Distance covered walking  = 4 \times 2.5  = 10 km  

Time to cover 10 km on cycle  = \frac{10 km \times hr}{12 km}  = \frac{5}{6} hr    or 50 minutes

 

Q5. A car can finish a certain journey in 10 hours at a speed of 48 km/hr. By how much the speed of car must be increased to cover the same distance in 8 hours?

Answer:

Distance covered by the car  = 48 \times 10 = 480 km

Speed to cover the same distance in 8 hr   =\frac{480 km}{8 hr} = 60 \frac{km}{hr} 

Hence the speed must be increased by   = 60 -48 = 12\hspace{2pt} \frac{km}{hr} 

 

Q6. A bus covers a certain distance in 50 minutes, if it runs at a speed of 54 km/hr. What must be the speed of the bus in order to reduce the time of journey to 40 minutes?

Answer:

Distance covered by the bus  = \frac{50}{60} \times 54 = 45 \frac{km}{hr} 

Speed to cover the same distance in 40 min   = \frac{45 km \times 60}{40 hr } = 67.5 \frac{km}{hr} 

 

Q7. A motor car starts with the speed of 70 km/hr with its speed increasing every two hours by 10 km/hr. In how much time will it cover a distance of 345 km?

Answer:

Speed at the start  = 70\frac{km}{hr} 

Distance covered in first 2 hours = 140 \frac{km}{hr} 

Speed After 2 hours = 80 \frac{km}{hr} 

Distance covered in 3rd and the 4th hour = 160 km

Total distance covered by end of 4th hours = 140 + 160 = 300 km

Distance left to be covered after end of 4th hour  = 345 - 300 = 45 km

Speed After 4 hours = 90 \frac{km}{hr} 

Time taken to cover 45 km at speed of  90 \frac{km}{hr} = 0.5 hr

Hence the total time to cover  345 km = 4.5 hr

 

Q8. A man takes 150 steps in walking 75 meters. If he takes 3 steps in 1 second, find his speed in (i) m/sec (ii) km/hr.

Answer:

Length of one step = \frac{75}{150} = 0.5 m  

Distance covered in 1 sec = 0.5\times3 = 1.5 \frac{m}{s} 

i) Speed in \frac{m}{s} = 1.5 \frac{m}{s} 

ii) Speed in \frac{km}{hr} = \frac{1.5 km \times 3600}{1000\times hr} = 5.4 \frac{km}{hr}  

 

Q9. A man walks at 5 km/hr for 6 hours and at 4 km/hr for 12 hours. Find his average speed.

Answer:

Average Speed  = \frac{Distance Covered}{Total time taken to cover the distance}  

Average Speed = \frac{5 \times 6 + 4 \times 12}{6 + 12}  = 4\frac{1}{3} \frac{km}{hr} 

 

Q10. A man covers a distance of 144 km at the speed of 36 km/hr and another 256 km at the speed of 64 km/hr. Find his average speed for the whole journey.

Answer:

Average Speed  = \frac{Distance Covered}{Total time taken to cover the distance}  

Average Speed = \frac{144 +256}{\frac{144}{36} + \frac{256}{64}}  = 50 \frac{km}{hr} 

 

Q11. Two buses travel to a place at 45 km/hr and 60 km/hr respectively. If the second bus takes   5\frac{1}{2} hr   hours less than the first for the same journey, find the length of the journey.

Answer:

Let  x   be the distance of the journey

Time taken by the First bus = \frac{x}{45} hr  

Time taken by the Second bus = \frac{x}{60} hr  

Therefore \colon  \frac{x}{45}-  \frac{x}{60} =  \frac{11}{2} 

Solving for  x = 990 km  

 

Q12. A boy goes to school from his village at 3km/hr and returns back at 2km/hr. If he takes 5 hours in all, what is the distance between the village and the school?

Answer:

Let  x   be the distance of the journey

Time taken to reach school = \frac{x}{3} hr  

Time taken return from = \frac{x}{2} hr  

Therefore \colon  \frac{x}{3} + \frac{x}{2} =  5

Solving for  x = 6 km  

 

Q13. A bus completes a journey of 420 km in  6\frac{1}{2} hr   . The first ¾ part of the journey performed at 63 km/hr.  Calculate the speed of the rest of the journey.

Answer:

Let  x   be the speed of the rest of the journey

\frac{3}{4} \times 420 \times \frac{1}{63} + \frac{105}{x} = 6\frac{1}{2}  

Solving for  x = 70  \frac{km}{hr}  

 

Q14. A man drives 150 km from town A to town B in 3 hours 20 min and returns back to town A from town B in 4 hours 10 min. Find his average speed for the whole journey.

Answer:

Average Speed  = \frac{Distance Covered}{Total time taken to cover the distance}  

Average Speed = \frac{150 + 150}{3\frac{1}{3} + 4\frac{1}{6}}  = 40 \frac{km}{hr} 

 

Q15. A car completed a journey in 7 hours.  One-third of the journey was performed at 20 km/hr and the rest at 30 km/hr. Find the total length of the journey.

Answer:

Let  x      be the distance of the journey.

\frac{\frac{x}{3}}{20} + \frac{\frac{2x}{3}}{30} = 7  

Solving for  x = 180 km   

 

Q16. A cyclist covered a certain distance in   3\frac{1}{2}   hours. The speed for first half of the distance was 15 km/hr and for the second half it was 20 km/hr. Find the total distance covered by him.

Answer:

Let  x      be the distance of the journey.

\frac{\frac{x}{2}}{15} + \frac{\frac{x}{2}}{20} = 3\frac{1}{2} 

Solving for  x = 60 km   

 

Q17. A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. Find the total distance.

Answer:

Let  x     be the distance of each leg

\frac{x}{3} + \frac{x}{4} + \frac{x}{5} = \frac{47}{60} 

Solving for  x = 1 km     and the total distance is   3 km   

 

Q18. A farmer traveled a distance of 61 km in 9 hours. He traveled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. Find the distance traveled by him on foot.

Answer:

Let  x     be the distance traveled by foot

\frac{x}{4} + \frac{61 - x}{9}  = 9 

Solving for  x = 16 km   

 

Q19. Rohan cycles to his office at the rate of 12\frac{1}{2}   km/hr and is late by 3 minutes. However, if he travels at 15 km/hr, he reaches 5 minutes earlier than the usual time. What is the distance of his office from his residence?

Answer:

Let  x     be the distance to office. The difference of the time in the two cases is 8 minutes.

\frac{x}{12.5} - \frac{x}{15}  = \frac{8}{60}

Solving for x=10 km     (Distance of his office from his residency)

 

Q20. Robert is travelling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr. However, he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?

Answer:

Let the distance traveled  = x km    

\frac{x}{10} - \frac{x}{15}  =2

Solving for x=60 km 

\frac{60}{10} - \frac{60}{s}  =1

Solving for s=12 \frac{km}{hr}

 

Q21. If a train runs at 40 km/hr, it reaches its destination late by 11 minutes, but if it runs at 50 km/hr, it is late by 5 minutes only. Find the correct time for the train to complete its journey.

Answer:

Let the distance traveled by the train  = x km    

\frac{x}{40} - \frac{x}{50}  = \frac{6}{60}

Solving for   x = 20 km       (Distance of his office from his residency)

Time taken to cover 20 km=30 minutes

Therefore the correct time is 19 minutes

 

Q22. The distance between Delhi and Hyderabad is 1800 km. A train leaves Delhi and proceeds towards Hyderabad at a uniform speed of 60 km/hr. Another train leaves Hyderabad at the same time and proceeds towards Delhi at a uniform speed of 48 km/hr. When and where will they meet?

Answer:

Let the train meet at a distance  = x km     from Delhi

 \frac{x}{60} = \frac{(1800-x)}{48}   

Solving for   x  = 1000 km     . The trains will meet 1000 km from Delhi.

Time taken before them meet = \frac{1000}{60} = 16\frac{2}{3} hr 

 

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