Time and Distance

REASONING AND QUANTITATIVE APTITUDE Time & Distance

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TIME &

DISTANCE


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MODULE OBJECTIVE:

Decision making for planning, policy, and management relies increasingly on quantitative reasoning, which entails the collection, analysis and interpretation of quantitative data. This course is designed to introduce principles and techniques to solve time and distance related problems.

Develop Logical Reasoning in a Problem-Solving Framework. One goal is to develop a disciplined logical analysis of “word” problems. Such reasoning is the foundation for building simple mathematical models of problems – models implicit in counting time and distance. A good way to learn this logical thinking is by working many exercises. Students will use this reasoning often (consciously or unconsciously) in computer science, operations research, and probability and statistics. However, a logical mind will serve a person well in ANY field. At the end of these course students:

• To be understood the types of formulae are used to measure time and Distance. • To be able to calculate time and distance while an object that moves at a constant

rate is said to be in uniform motion, Uniform motion problems may involve objects going the same direction, opposite directions, or round trips.

• To be solving many problems related to time and distance and which can be useful to students to face interviews.

C. PREREQUISITIES (Important Formulas):

i) Speed = Distance/Time ii) Time = Distance/speed

iii) Distance = speed*time iv) 1km/hr = 5/18 m/s v) 1 m/s = 18/5 Km/hr

vi) If the ratio of the speed of A and B is a:b,then the ratio of the time taken by them to cover the same distance is 1/a : 1/b or b:a

vii) suppose a man covers a distance at x kmph and an equal distance at y kmph.then the average speed during the whole journey is (2xy/x+y) kmph

viii) An object that moves at a constant rate is said to be in uniform motion. The formula d = rt gives the relationship between distance d, rate r, and time t. Uniform motion problems may involve objects going the same direction, opposite directions, or round trips.


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D. Solved Examples: 1.) Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in. A. 12 min B. 25 min C. 40min D. 60 min

Answer: Option C

Explanation: Distance = Speed * time 4*11/4 = 11km New Speed = 16.5 kmph Therefore time = D/S = 11/16.5 = 40min

2.) A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be. A. 45 min B. 60 min C. 75 min D. None of these

Answer: Option B

Explanation: Time = 50/60 hr = 5/6hr Speed = 48mph distance = S*T = 48 * 5/6 = 40km time = 40/60hr = 2/3hr New speed = 40* 3/2 kmph = 60kmph

3.) Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction? A. 17 hrs B. 25 hrs C. 31 hrs D. 45 hrs

Answer: Option A

Explanation:

The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph

Distance between them is 8.5 km Time= 8.5km / 0.5 kmph = 17 hrs

4.) Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? A. 4 B. 6 C. 8 D. None of these

Answer: Option D

Explanation: Due to stoppages, it covers 9 km less. Time taken to cover 9 km = (9/54 x 60) min = 10 min.


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5.) 2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other at a distance of 110km from one of the stations. What is the ratio of their speeds? A. 7:3 B. 11:9 C. 18:4 D. None of these

Answer: Option B

Explanation: In same time, they cover 110km & 90 km respectively so ratio of their speed =110: 90 = 11: 9

6.) In covering a distance of 30 km, Sachin takes 2 hours more than Rohit. If Sachin doubles his speed, then he would take 1 hour less than Rohit. Sachin speed is: A. 5 kmph B. 16 kmph C. 21 kmph D. None of these

Answer: Option A

Explanation: Let Sachin’s speed be X km/hr. Then, 30/x - 30/2x = 3 6x = 30 x = 5 km/hr.

7.) A train 140m long running at 60kmph. In how much time will it pass a platform 260m long? A. 5 kmph B. 16 kmph C. 21 kmph D. None of these

Answer: Option A

Explanation: Distance travelled = 140 + 260m = 400m, Speed = 60 * 5/8 = 50/3m Time = 400 * 3/50 = 24 Seconds

8.) The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4 hours, then the speed of the first train is: A. 47.4 km/hr B. 57.19 km/hr C. 68.13 km/hr D. None of these

Answer: Option D

Explanation: Let the speed of two trains be 7x and 8x km/hr. Then, 8x = (440/4) = 110 x = (110/8) = 13.75 Speed of first train = (7 x 13.75) km/hr = 96.25 km/hr.


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9.) Sachin can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 kmph and the rest at 5kmph.the total distance is? A. 5km B. 6km C. 7km D. 8km

Answer: Option D

Explanation: Distance = 2/3S distance=1-2/3S=1/3S 21/15 hr=2/3 S/4 + 1/3s /5 84=14/3S * 3 S= 6km

10.) A person walks at 5kmph for 6hr and at 4kmph for 12hr.The average speed is. A. 4 1/3 B. 7 2/3 C. 9 ½ km D. 8km

Answer: Option D

Explanation: Avg speed = total distance/total time = 5*6 + 4*12 / 18 =4 1/3 mph

11)A person covers a certain distance at 7kmph .How many meters does he cover in 2 minutes. A) 14 kmph B) 7 kmph C) 2400m D) 1200m

Answer: Option C

Explanation: Speed=72kmph=72*5/18 = 20m/s Distance covered in 2min =20*2*60 = 2400m

12)If a man runs at 3m/s. How many km does he run in 1hr 40min A) 18 km B) 7 km C) 12 km D) 17 km

Answer: Option A

Explanation: Speed of the man = 3*18/5 kmph = 54/5kmph Distance covered in 5/3 hrs=54/5*5/3 = 18km

13)A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The speed at which the train must run to reduce the time of journey to 40min will be. A) 18 kmph B) 60 km ph C) 30 kmph D) 50 kmph

Answer: Option B


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Explanation: Time=50/60 hr=5/6hr Speed=48mph distance=S*T=48*5/6=40km time=40/60hr=2/3hr New speed = 40* 3/2 kmph= 60kmph

14)Vikas can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 kmph and the rest at 5kmph.the total distance is? A) 18 km B) 6 km C) 12 km D) 17 km

Answer: Option B

Explanation:

Let total distance be S total time=1hr24min A to T :: speed=4kmph diistance=2/3S T to S :: speed=5km distance=1-2/3S=1/3S 21/15 hr=2/3 S/4 + 1/3s /5 84=14/3S*3 S=84*3/14*3 = 6km

15)walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. A) 4 B) 7 ½ C) 7 D) 5

Answer: Option B

Explanation:

Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½


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E. EXERCISE PROBLEMS: 1)A man covers a distance on scooter .had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower he would have taken 40min more.the distance is. Solution::

Let distance = x m Usual rate = y kmph x/y – x/y+3 = 40/60 hr 2y(y+3) = 9x ————–1 x/y-2 – x/y = 40/60 hr y(y-2) = 3x —————–2 divide 1 & 2 equations by solving we get x = 40

2)Excluding stoppages, the speed of the bus is 54kmph and including stoppages, it is 45kmph.for how many min does the bus stop per hr.

Solution::

Due to stoppages,it covers 9km less. time taken to cover 9 km is [9/54 *60] min = 10min

3)Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. what time will they take to be 8.5km apart, if they walk in the same direction. Solution::

The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph Distance between them is 8.5 km Time= 8.5km / 0.5 kmph = 17 hrs

4)2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other at a distance of 110km from one of the stations. what is the ratio of their speeds.

Solution::

In same time ,they cover 110km & 90 km respectively so ratio of their speed =110:90 = 11:9


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5)Two trains start from A & B and travel towards each other at speed of 50kmph and 60kmph resp. At the time of the meeting the second train has traveled 120km more than the first.the distance between them.

Solution::

Let the distance traveled by the first train be x km then distance covered by the second train is x + 120km x/50 = x+120 / 60 x= 600 so the distance between A & B is x + x + 120 = 1320 km

6)A thief steals a ca r at 2.30pm and drives it at 60kmph. The theft is discovered at 3pm and the owner sets off in another car at 75kmph when will he overtake the thief Solution::

Let the thief is overtaken x hrs after 2.30pm distance covered by the thief in x hrs = distance covered by the owner in x-1/2 hr 60x = 75 ( x- ½) x= 5/2 hr thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm

7) In covering distance, the speed of A & B are in the ratio of 3:4.A takes 30min more than B to reach the destination. The time taken by A to reach the destination is. Solution::

Ratio of speed = 3:4 Ratio of time = 4:3 let A takes 4x hrs,B takes 3x hrs then 4x-3x = 30/60 hr x = ½ hr Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr

8)A person covers a certain distance at 7kmph .How many meters does he cover in 2 minutes. Solution:: speed=72kmph=72*5/18 = 20m/s distance covered in 2min =20*2*60 = 2400m


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9)If a man runs at 3m/s. How many km does he run in 1hr 40 min Solution::

speed of the man = 3*18/5 kmph = 54/5kmph Distance covered in 5/3 hrs=54/5*5/3 = 18km

10)Walking at the rate of 4knph a man covers certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in. Solution::

Distance=Speed* time 4*11/4=11km New speed =16.5kmph therefore Time=D/S=11/16.5 = 40min

11)A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The speed at which the train must run to reduce the time of journey to 40min will be. Solution::

Time=50/60 hr=5/6hr Speed=48mph distance=S*T=48*5/6=40km time=40/60hr=2/3hr New speed = 40* 3/2 kmph= 60kmph

12)A man covers a distance on scooter .had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower he would have taken 40min more. the distance is. Solution::

Let distance = x m Usual rate = y kmph x/y – x/y+3 = 40/60 hr 2y(y+3) = 9x -------------------------------------------------1 x/y-2 – x/y = 40/60 hr y(y-2) = 3x ------------------------2 divide 1 & 2 equations by solving we get x = 40

13)Excluding stoppages,the speed of the bus is 54kmph and including stoppages, it is 45kmph.for how many min does the bus stop per hr. Solution::

Due to stoppages, it covers 9km less. time taken to cover 9 km is [9/54 *60] min = 10min

14)A motorist covers a distance of 39km in 45min by moving at a speed of xkmph for the first 15min.then moving at double the speed for the next 20 min and then again moving at his original speed for the rest of the journey .then x=?


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Solution:: Total distance = 39 km Total time = 45 min D = S*T x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km x = 36 kmph

15)A & B are two towns. Mr.Fara covers the distance from A to B on cycle at 17kmph and returns to A by a tonga running at a uniform speed of 8kmph.his average speed during the whole journey is. Solution:: When same distance is covered with different speeds, then the average speed = 2xy / x+y =10.88kmph 16)A car covers 4 successive 3km stretches at speed of 10kmph,20kmph,30kmph & 60kmph resp. Its average speed is. Solution::

Average speed = total distance / total time total distance = 4 * 3 = 12 km total time = 3/10 + 3/20 + 3/30 + 3/60 = 36/60 hr speed =12/36 * 60 = 20 kmph

17)A person walks at 5kmph for 6hr and at 4kmph for 12hr. The average speed is. Solution::

avg speed = total distance/total time = 5*6 + 4*12 / 18 =4 1/3 mph

18)A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time.wht should be its speed to cover the remaining distance in the time left. Solution::

Time left = 10 – 3/5*10 = 4 hr speed =40 km /4 hr =10 kmph

19)The ratio between the speeds of the A& B is 2:3 an therefore A takes 10 min more than the time taken by B to reach the destination. If A had walked at double the speed ,he would have covered the distance in ? Solution::

Ratio of speed = 2:3 Ratio of time = 3:2 A takes 10 min more


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3x-2x = 10 min A time=30 min

A covers the distance in 30 min , if its speed is x -> He will cover the same distance in 15 min, if its speed doubles (i.e 2x)

20)A is twice as fast as B and B is thrice as fast as C is. The journey covered by B in? Solution::

speed& ratio a : b = 2: 1 b : c = 3:1 Time& ratio b : c = 1:3 b : c = 18:54 (if c covers in 54 min i..e twice to 18 min )

21)A man performed 3/5 of the total journey by ratio 17/20 by bus and the remaining 65km on foot.wht is his total journey. Solution::

Let total distance is x x-(3/5x + 17/20 x) =6.5 x- 19x/20 = 6.5 x=20 * 6.5 =130 km

22)A train M leaves Meerat at 5 am and reaches Delhi at 9am . Another train N leaves Delhi at 7am and reaches Meerut at 1030am At what time do the 2 trains cross one Another Solution::

Let the distance between Meerut & Delhi be x they meet after y hr after 7am M covers x in 4hr N covers x in 3 ½ i.e 7/2 hr speed of M =x/4 speed of N = 2x/7 Distance covered by M in y+2 hr + Distance covered by N in y hr is x x/4 (y+2) +2x/7(y)=x y=14/15hr or 56 min

23)A man takes 5hr 45min in walking to certain place and riding back. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is? Solution::

Let x be the speed of walked Let y be the speed of ride


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Let D be the distance Then D/x + D/y = 23/4 hr -------------------------1 D/y + D/y = 23/4 – 2 hr D/y = 15/8 -------------------------------------------2 substitute 2 in 1 D/x + 15/8 = 23/4 D/x = 23/4 -15/8 =46-15/8 =31/8 Time taken for walk one way is 31/8 hr time taken to walk to and fro is 2*31/8 = 31/4 hr =7 hr 45 min

24. EngineeringA train leaves a train station at 1 p.m. It travels at an average rate of 60 mi/h. A high-speed train leaves the same station an hour later. It travels at an average rate of 96 mi/h. The second train follows the same route as the first train on a track parallel to the first. In how many hours will the second train catch up with the first train?

Solution:

25. Noya drives into the city to buy a software program at a computer store. Because of traffic conditions, she averages only 15 mi/h. On her drive home she averages 35 mi/h. If the total travel time is 2 hours, how long does it take her to drive to the computer store?


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26. Jane and Peter leave their home traveling in opposite directions on a straight road. Peter drives 15 mi/h faster than Jane. After 3 hours, they are 225 miles apart. Find Peter's rate and Jane's rate.

27.A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? A. 3.6 B.7.2 C. 8.4 D.10

Answer: Option B


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Explanation:

Speed=(600/5 * 60) m/sec

= 2 m/sec.

Converting m/sec to km/hr (see important formulas section)

=(2*18/5) km/hr

= 7.2 km/hr.

28. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover

the same distance in 1 hours, it must travel at a speed of: A. 300 kmph B.360 kmph C. 600 kmph D.720 kmph

Answer: Option D

Explanation:

Distance = (240 x 5) = 1200 km.

Speed = Distance/Time

Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]

Required speed =(1200 * 3/5) km/hr= 720 km/hr.

29. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more.

The actual distance travelled by him is: A. 50 km B.56 km C. 70 km D.80 km

Answer: Option A

Explanation:

Let the actual distance travelled be x km.

Then x/10=(x+20)/14

14x = 10x + 200 4x = 200 x = 50 km.


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30. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is: A. 100 kmph B.110 kmph C. 120 kmph D.130 kmph

Answer: Option C

Explanation:

Let speed of the car be x kmph.

Then, speed of the train=(150/100)*x=(3/2)*x kmph

(75/x)-(75/(3/2x))=125/(10*60)

(75/x)-(50/x)=5/24

x = 25 x24 = 120 kmph. 5

31. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45

kmph. For how many minutes does the bus stop per hour? A. 9 B.10 C. 12 D.20

Answer: Option B

Explanation:

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km =9

x 60min

= 10 min.54

32. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is: A. 1 hour B.2 hours C. 3 hours D.4 hours

Answer: Option A

Explanation:

Let the duration of the flight be x hours.

Then, 600- 600 = 200


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x x + (1/2)

600- 1200 = 200x 2x + 1

x(2x + 1) = 3

2x2 + x - 3 = 0

(2x + 3)(x - 1) = 0

x = 1 hr. [neglecting the -ve value of x]

33. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. A. 220 km B.224 km C. 230 km D.234 km

Answer: Option B

Explanation:

(1/2)x+ (1/2)x= 1021 24 x + x = 2021 24

15x = 168 x 20

x = 168 x 20 = 224 km. 15

34. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms 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: Option D

Explanation:

Let the speed of two trains be 7x and 8x km/hr.

Then, 8x = 400 = 1004

x = 100 = 12.58


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Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

35. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is: A. 35.55 km/hr B.36 km/hr C. 71.11 km/hr D.71 km/hr

Answer: Option C

Explanation:

Total time taken =160

+160

hrs.=

9hrs.64 80 2

Average speed = 320 x2

km/hr= 71.11 km/hr.9

36.

A car travelling with of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

A. 176km/hr7

B.25 km/hr

C. 30 km/hr D.35 km/hr

Answer: Option D

Explanation:

Time taken = 1 hr 40 min 48 sec = 1 hr 404min = 151hrs =126hrs.5 75 75

Let the actual speed be x km/hr.

Then, 5x x126= 427 75

x = 42 x 7 x 75 = 35 km/hr.5 x 126

37. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is: A. 5 kmph B.6 kmph C. 6.25 kmph D.7.5 kmph

Answer: Option A

Explanation:


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Let Abhay's speed be x km/hr.

Then, 30-30= 3x 2x

6x = 30

x = 5 km/hr.

38. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.? A. 8 kmph B.11 kmph C. 12 kmph D.14 kmph

Answer: Option C

Explanation:

Let the distance travelled by x km.

Then, x - x = 210 15

3x - 2x = 60

x = 60 km.

Time taken to travel 60 km at 10 km/hr =60

hrs= 6 hrs.10

So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

Required speed = 60

kmph.= 12 kmph.5

39. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by

car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is: A. 2 : 3 B.3 : 2 C. 3 : 4 D.4 : 3

Answer: Option C

Explanation:

Let the speed of the train be x km/hr and that of the car be y km/hr.


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Then, 120+480= 8 1+4= 1 ....(i)x y x y 15

And, 200+400=25 1+ 2= 1 ....(ii)x y 3 x y 24

Solving (i) and (ii), we get: x = 60 and y = 80.

Ratio of speeds = 60 : 80 = 3 : 4.

40. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is: A. 14 km B.15 km C. 16 km D.17 km

Answer: Option C

Explanation:

Let the distance travelled on foot be x km.

Then, distance travelled on bicycle = (61 -x) km.

So, x +(61 -x)= 9 4 9

9x + 4(61 -x) = 9 x 36

5x = 80

x = 16 km.

41. A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

A. 35 B.3623

C. 3712

D.40

Answer: Option D

Explanation:

Let distance = x km and usual rate = y kmph.

Then, x- x =40 2y(y + 3) = 9x ....(i) y y + 3 60

And, x -x=40 y(y - 2) = 3x ....(ii) y -2 y 60


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On dividing (i) by (ii), we get: x = 40.

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

• Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

• Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

• Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.

• Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.

• Give answer(E) if the data in both Statements I and II together are necessary to answer the question.

42. Two towns are connected by railway. Can you find the distance between them? I. The speed of the mail train is 12 km/hr more than that of an express train.

II. A mail train takes 40 minutes less than an express train to cover the distance.

A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

Answer: Option D

Explanation:

Let the distance between the two stations be x km.

I. Then, speed of the mail train = (y + 12) km/hr.

II.x- x =40.y (y + 12) 60

Thus, even I and II together do not give x.

Correct answer is (D).


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43. The towns A, B and C are on a straight line. Town C is between A and B. The distance from A to B is 100 km. How far is A from C?

I. The distance from A to B is 25% more than the distance from C to B. II.

The distance from A to C is of the distance C to B.


Answer: Option C

Explanation:

.__________.______________________________________. A x C (100 - x) B

Let AC = x km. Then, CB = (100 -x) km.

I. AB = 125% of CB

100 = 125x (100 - x)100

100 - x = 100 x 100= 80125

x = 20 km.

AC = 20 km.

Thus, I alone gives the answer.

II. AC = 1CB4

x = 1(100 - x)4

x = 100

x = 20.

AC = 20 km.

Thus, II alone gives the answer.

Correct answer is (C).


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44. Two cars pass each other in opposite direction. How long would they take to be 500

km apart? I. The sum of their speeds is 135 km/hr.

II. The difference of their speed is 25 km/hr.


Answer: Option A

Explanation:

I gives, relative speed = 135 km/hr.

Time taken = 500hrs. 135

II does not give the relative speed.

I alone gives the answer and II is irrelevant.

Correct answer is (A).

45. How much time did X take to reach the destination? I. The ratio between the speed of X and Y is 3 : 4.

II. Y takes 36 minutes to reach the same destination.


Answer: Option E

Explanation:

Since ratio of speed of X : Y is 3 : 4, then ratio of time will be 4 : 3.

I. If Y takes 3 min, then X takes 4 min.

II. If Y takes 36 min, then X takes 4x 36

min= 48 min.3

Thus, I and II together give the answer.

Correct answer is (E).


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F. QUESTION BANK MOCK TEST 1. Express a speed of 54 km/hr in meters/second. a)15 m/sec b)20 m/sec c)25 m/sec d)30 m/sec

2.A car can cover 350 km in 4 hours. If the speed is decreased by 12 1/2 kmph, how much

time does the car take to cover a distance of 450 km?

a)4 hrs b)5 hrs c)2 hrs d)6 hrs

3.A person covers a certain distance at a certain speed. If he increases his speed by 25 %

then he takes 12 minutes less to cover the same distance. Find the time taken by him

initially to cover the distance at the original speed

a)3 hrs b)2 hrs c)1 hr d)7 hrs

4.A car covers a certain distance going at a speed of 60 kmph and returns to the starting

point at a speed of 40 kmph.Find the average speed for the whole journey.

a)48 kmph b)42 kmph c)34 kmph d)40 kmph

5.What is the time taken by a train running at 54 km/hr to cross a man standing on a

platform, the length of the train being 180 m?

a)6 seconds b)12 seconds c)16 seconds d)18 seconds

6.How long will a train 100 m long and travelling at a speed of 45 kmph,take to corss a

platform of length 150 m?

a)20 sec b)29 sec c)27 sec d)cannot be determined

7.Find the length of the bridge,which a train 120 m long travelling at 54 kmph can cross

in 30 seconds.

a)340 m b)350 m c)330 m d)390 m


24 SITAMS

8.A worker reaches his work place 15 minutes late by walking at 4kmph from his house.

The next day he increases his speed by 2kmph and reaches in time. Find the distance from

his house to his work place

a)2 km b)6 km c)8 km d)3 km

9.A person leaves his house and travelling at 4 kmph reaches his office 10 minutes late.

Had he travelled at 7kmph he would have been 20 mins early. Find the distance from the

house to the office?

a)14/3 b)2 c)14/9 d)14/6

10.Find the time taken by a train 150 m long running at a speed of 63 kmph to cross

another train of length 100 m long running at a speed of 45 kmph in the same direction


11.A train crosses two persons, cycling in the same direction as the train in 12 and 18

seconds respectively. If the speeds of the two cyclists are 9 and 18 kmph respectively.

Find the length and speed of the train.

a)80 m b89 m c)98 m d)90 m

12.Two trains running at 45 and 54 kmph cross each other in 12 seconds when they run in

opposite directions. When they run in the same direction, a person in the faster train

observes that he crossed the other train in 32 seconds. Find the lengths of the two trains

a)250 b)450 c)260 d)234

13.Two trains of length 150 m and 250m run on parallel lines. When they run in the same

direction it will take 20 seconds to cross each other and when they run in opposite

direction it will take 5 seconds. Find the speeds of the two trains.

a)180 and 108 b)272 and 211 c)123 and 828 d)none of these


25 SITAMS

14.The average speed for an entire journey is 60 kmph without considering the stoppages.

When the stoppages are considered the average speed becomes 48 kmph. How many

minutes per hour on an average were the stoppages?

a)10 mins b)12 mins c)16 mins d)none of these

15.I had to catch a bus which was 225 m ahead of me. The bus also started at the same

time. If the speed of the bus was 2.5 m/sec and my speed was 36 kmph, in how much time

can i catch the bus?


16.The distance from my house to my friends house is 12 km. I walked at a speed of 4

kmph and after every kilometre took rest for 10 mins.How much time did it take for me to

reach my friends house?

a)3 hrs b)4 hrs and 50 mins c)5 hrs d)none of these

17.A train covered a distance of 250 km,partly at an average speed of 40 kmph and partly

at 60 kmph. Find the distance covered at 40 kmph if it took 5 hrs for the train to cover the

distance.

a)150 km b)120 km c)100km d)cannot be determined

18.A bus covered a distance of 160 km in 4 hrs covering a part of it at 30 kmph and the

remaining at 70 kmph.For how much time did the us travel at 70 kmph?

a)0.5 hr b)1 hr c)1 1/2 hs d)2 hrs

19.A car takes 2 hours more to cover a distance of 480 km when its speed is reduced by 8

kmph. Find its usual speed



26 SITAMS

20.A person covered the first 40 km of his journey at 50 kmph,the next 70 km at 35 kmph

and the remaining distance in 12 mins. If the average speed of the entire journey is 52

kmph. Find the distance covered in the last stench of the journey.

a)22 km b)34 km c)40 km d)46 km

21.A train takes 10 seconds to cross a man standing on a platform and 44 seconds to cross

the platform. What is the length of the platform. What is the length of the platform if the

speed of the train is 72 kmph?

a)440 m b)570 m c)680 m d)none of these

22.A train travelling at 36 kmph takes 48 seconds to cross a bridge. It then crosses a man

cycling at the rate of 9 kmph in the same direction in 20 seconds. Find the length of the

bridge

a)150 m b)220 m c)280 m d)330 m

23.A train crosses two bridges 370 m and 480 m long in 51 and 62 seconds respectively.

Find the speed of the train.


24.A man started 15 minutes late and by travelling at a speed which is 5/4rth of his usual

speed reached his office 20 mins early. What is the usual time of the journey?

a)85mins b)100 mins c)135 mins d)175 mins

25.A parachutist,before he opens his parachute,falls for a time t1,and covers a distance of

5t1^2 and after he opens his parachute he falls for a time t2 and covers a distance Vt2.V is

the velocity attained just before the parachute is opened and is given by 5t1.After what

time did he open the parachute,if the total distance covered by the parachutist is 1500m

and the total time is 30 seconds?



27 SITAMS

26.Akash,Anurag and Rishab are running around a circular track of length 900 m with

respective speeds of 15 m , 20 m and 30 m/sec.Akash and Anurag are running in the same

direction while Rishab is running in the opposite direction.After how much time will all

the three of them meet for the first time?


27.A police patrol party travelling at 60 kmph crosses an escaping thief travelling in the

opposite direction at 48 kmph.The police party has to travel for a further 5 minutes before

it can find a gap in the median where it can take a U turn and start chasing the thief.After

how much time after the police party crosses the thief does it catch him?

a)25 mins b)50 mins c)15 mins d)32 mins

28.In a 1000 m race A reaches the goal 5 seconds earlier and beats B by 50 m.What is A's

speed?

a)10 m/s b)10 10/19 m/s c)9 9/19 m/s d)11 9/19 m/s

29.Two points A and B are diametrically opposite points on a circular road of

circumference 12 km. A cyclist started from A and made three rounds.He made the first

round with a speed of 12 kmph and decreased his speed by 3 kmph for every round.What

is the interval between the first time he passes through B and the third time he passes

through B?

a)200 mins b)100 mins c)85 mins d)170 mins

30.Two men left simultaneously two places A and B.One of them left A for B while the

other left B for A.Both travel each at his own uniform velocity.The first person on

reaching B returns to A and then again travels bach to B and so on.What will be the

distance covered by the first person when they meet for the third time given the ratio of

the speed of the first person to that of the second person is 3:2 the distance between A and

B is 500 m?

a)1000 m b)1500 m c)2500 m d)1200 m


28 SITAMS

31.A person takes 6 hours to go by car to a certain place and return by bus.He gains 2 hrs

if he goes both ways by car.How long would he have taken if he had gone by bus both

ways?

a)4 hrs b)6 hrs c)8 hrs d)2 hrs

32.car A and car B are travelling on two perpendicular roads towards city C with equal

speeds. car A starts from a distance of 100 km ar 11 a.m while car B starts from a

distance of 70 km at 12 noon. At 2p.m the two cars are 50 km apart. What is the speed

with which they are travelling?


33.Two trains of length 200 m and 100 m simultaneously wnter a tunnel of length 300m

from opposite ends at the same time on parallel tracks.The respective speeds of the two

trains are 36 kmph and 18 kmph.After how much time from the instant the two trains

entered the tunnel will the tunnel be free of traffic again?


34.Rajat had covered one third of the total distance of his trip when his scooter failed .He

then parked it and covered the remaining distance on foot, spending 20 times as long

walking as riding. How many times was his riding speed more than his walking speed?

a)20 b)19 c)10 d)9

35.Ashish and Bali run towards each other from P and Q respectively with respective

speeds of 36 kmph and 45 kmph.After meeting each other if Ashish reaches Q in 5

hours,in how many hours will Bali reach P?

a)3 b)3 1/5 c)4 d)8


29 SITAMS

36.A train of length 180 m travelling at 72 kmph overtook a motorcyclist travelling at 36

kmph at 4 p.m. At 5 p.m it overtook another cyclist travelling in the opposite direction at

a speed of 18 kmph.When will the cyclist meet the motorcyclist?

a)1 hr 20 mins b)1 hr 30 min c)1 hr 45 min d)none of the above

37.Two men left simultaneously two places A and B. one of them left A for B and the

other B for A. Both travelled each with his own uniform velocity. Having arrived at their

destination, they turned back without stopping and turned back to their starting points.

First time, they met on their own journey 18 km from B; the second time on their return

journey 9 km from A. Find the distance AB.

a)30 km b)45 km c)60 km d)cannot be determined

38.A car travels a total distance of 150 km. After travelling a part of the distance without

any trouble ,the car develops an engine problem and proceeds at 2/3rd of its former speed

and arrives at the destination 48 mins late. Had the problem developed 24 km further on,

the car would have arrived 12 min sooner. Find the original distance it travelled without

any problem and the speed over that part of the journey.

a)100km,60 kmph b)48km,36kmph c)72km,50kmph d)54km,60 kmph

39. Two cyclists simultaneously start from A to B and B to A respectively. They cross

each other after a time t hours. The first person reaches B in another t1 hours while the

second person reaches A in another t2 hours. Then

a)t=t1+t2/2 b)t=2t1t2/t1+t2 c)t=sqrt(t1t2) d)t=t2-t1/2

40.Ramu starts from P towards Q at a speed of 30 kmph and after every 12 min increase

his speed by 5 kmph. If the distance between P and Q is 52 km, then how much time does

he take to cover the distance?

a)60 min b)72 min c)90 min d)120 min

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Time and Distance