Previous Year CAT Questions on Time Speed and Distance

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Previous Year CAT Questions on Time Speed and Distance

Download important CAT Time Speed and  Distance Questions  with Solutions PDF based on previously asked questions in CAT exam. Practice Time Speed and  Distance Questions with Solutions for CAT exam.

Instructions

DIRECTIONS for the following three questions: Answer the questions on the basis of the information given below.

A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of $30\pi$ km/hr on the OR road, 20$\pi$ km/hr on the IR road, and 15$\sqrt5$ km/hr on all the chord roads.

Question 1: Amit wants to reach E2 from N1 using first the chord N1 – W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question?

a) 60

b) 45.

c) 90

d) 105

Instructions

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Question 2: At what time do Ram and Shyam first meet each other?

a) 10 a.m.

b) 10:10 a.m.

c) 10:20 a.m.

d) 10:30 a.m.

Question 3: Amarendra and Dharmendra are brothers. One day they start at the same time from their home for Tatanagar railway station in their respective cars. Amarendra took 25 minutes to reach the station. After reaching the station Amarendra found that Dharmendra is 2500 m away from the station. The distance of Tatanagar Station from their home is 15 km. Next day Dharmendra decided to start 7 minutes early. If they drive at the speed same as the previous day then Amarendra will reach the station

a) 120 seconds earlier than Dharmendra

b) 120 seconds later than Dharmendra

c) 300 seconds earlier than Dharmendra

d) 300 seconds later than Dharmendra

e) at the same time with Dharmendra

Question 4: Pradeep could either walk or drive to office. The time taken to walk to the office is 8 times the driving time. One day, his wife took the car making him walk to office. After walking 1km, he reached a temple when his wife called to say that he can now take the car. Pradeep figure that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office.

a) 1

b) 7/3

c) 9/7

d) 16/7

e) 16/9

Question 5: A ferry carries passengers to Rock of Vivekananda and back from Kanyakumari. The distance of Rock of Vivekananda from Kanyakumari is 100km. One day, the ferry started for Rock of Vivekananda with passengers on board, at a speed of 20 km per hour. After 90 minutes, the crew realized that there is a hole in the ferry and 15 gallons of sea water had already entered the ferry. Sea water is entering the ferry at the rate of 10 gallons per hour. It requires 60 gallons of water to sink the ferry. At what speed should the driver now drive the ferry so that it can reach the Rock of Vivekananda and return back to Kanyakumari just in time before the ferry sinks? (Current of the sea water from Rock of Vivekananda to Kanyakumari is 2km per hour.)

a) 40 km/hr towards the Rock & 39 km/hr while returning to Kanyakumari

b) 41 km/hr towards the Rock & 38 km/hr while returning to Kanyakumari

c) 42 km/hr towards the Rock & 36 km/hr while returning to Kanyakumari

d) 35 km/hr towards the Rock & 39 km/hr while returning to Kanyakumari

Question 6: A ping pong ball is dropped from a 45 metres high multi-storey building. The ball bounces back three fifth of the distance each time before coming to rest. The total distance traversed by the ball is:

a) 150 m

b) 180 m

c) 175 m

d) None of the above

Question 7: Sukriti and Saloni are athletes. Sukriti covers a distance of 1 km in 5 minutes and 50 seconds, while Saloni covers the same distance in 6 minutes and 4 seconds. If both of them start together and run at uniform speed, by what distance will Sukriti win a 5 km mini marathon:

a) 150 m

b) 200 m

c) 175 m

d) 225 m

Question 8: The average speed of a bus is three-fifth the average speed of a car which covers 3250 kms, in 65 hours. What is the average speed of the bus ?

a) 30 kmph

b) 20 kmph

c) 35 kmph

d) 36 kmph

e) None of these

Question 9: A 360 metres long train crosses a platform in 120 seconds. What is the speed of the train ?

a) 3 m/s

b) 5 m/s

c) 4.5 m/s

d) Cannot be determined

e) None of these

Question 10: A 480 metre long train crosses a platform in 140 seconds. What is the speed of the train?

a) 5m/s

b) 7m/s

c) 4.5 m/s

d) Cannot be determined

e) None of these,

Let the radii of 2 circles be R and r respectively such that R=2*r. Triangle O$N_2$$E_1$and all the other 3 similar triangles form a right angle at the centre . So using pythagoras theorem the value of chords come out to be $\sqrt5$ * R/2 . Hence the total distance traveled is $\sqrt5$ * R/2 + 0.5*R*pi. Total time required can be calculated by distance / speed which comes out to be 3.5*R. Among options only 105 is integral multiple of 3.5.

Let the time at which they meet be t minutes past 10.

So, distance run by Ram + distance run by Shyam = 10 km

=> (60+t)5/60 [t+60 because he would have traveled for 9 am to 10 am and t minutes more before meeting Shyam]+ (15+t)*10/60 [15+t because he would have traveled from 9:45 to 10:00 and t minutes more]= 10

=> 300+5t+150+10t = 600 => t = 10

So, they meet at 10.10 am

Amarendra took 25 minutes to cover 15 km. In the same time Dharmendra travel 2500m less, i,e, 12.5 km

=> Speed of Amarendra = $\frac{15}{25} = 0.6$ km/min

Speed of Dharmendra = $\frac{12.5}{25} = 0.5$ km/min

=> Time taken by Dharmendra to reach the station = $\frac{15}{0.5} = 30$ minutes

Next day, Dharmendra started 7 minutes early, so he will reach the station = 30 – 25 – 7 = -2 minutes

=> 2 minutes or 120 seconds before Amarendra.

Let walking speed = $a$

=> Driving speed = $8a$

Let the distance between temple and office = x

Acc. to ques,

=> $\frac{x}{a} = \frac{1}{a} + \frac{x + 1}{8 a}$

=> $8x = 8 + x + 1$

=> $x = \frac{9}{7}$

The ferry must have traveled 1.5*(20-2) = 27 kms already. The ferry needs to cover 73 kms to reach Rock of Vivekananda and 100 kms back to Kanyakumari. 15 gallons of water has already entered the ship. 45 more gallons will enter in order for the ship to sink. So it takes 4.5 hours. The ferry has to travel 70 km and return 100 km before it sinks. Speed of stream from Rock memorial to Kanniyakumari is 2 km/hr

Check the options.

Option 1: $\frac{73}{38}+\frac{100}{41} = 4.36$
Option 2: $\frac{73}{39}+\frac{100}{40} = 4.37$
Option 3 : $\frac{73}{40}+\frac{100}{38} = 4.46$
Option 4: $\frac{73}{33}+\frac{100}{41} = 4.65$
Thus, the closest option is option C.
Hence, option C is the correct answer.

Take a free mock test for CAT

When the ball is dropped from 45m height it will cover a distance of 45m while going down after rebound it’ll cover a distance of $45*\frac{3}{5}$ while going up and a distance of $45*\frac{3}{5}$ while going down again. after 2nd rebound it’ll cover a distance of $45*\frac{3}{5}*\frac{3}{5}$ while going up and a distance of $45*\frac{3}{5}*\frac{3}{5}$ while going down again and so on

i.e. total distance traveled by the ball is 45 + $45*\frac{3}{5}$ + $45*\frac{3}{5}$ + $45*\frac{3}{5}*\frac{3}{5}$ + $45*\frac{3}{5}*\frac{3}{5}$ +………..

this form 2 infinite GPs as 45 + $45*\frac{3}{5}$ + $45*\frac{3}{5}*\frac{3}{5}$+……. and $45*\frac{3}{5}$+$45*\frac{3}{5}*\frac{3}{5}$+….

For 1st GP a=45 and r=$\frac{3}{5}$ therefore sum of this infinite GP is $\frac{45}{1-\frac{3}{5}}$ = $\frac{225}{2}$

For 2nd GP a=45*$\frac{3}{5}$  and r=$\frac{3}{5}$ therefore sum of this infinite GP is  $\frac{45*\frac{3}{5}}{1-\frac{3}{5}}$ = $\frac{145}{2}$

Therefore our answer = $\frac{225}{2}+\frac{145}{2}$ = 180 m i.e. option ‘B’

Sukriti covers a distance of 1 km in 5 minutes and 50 seconds therefore will cover 5 kms in 25 mins 250 secs = 29.16 mins

Saloni covers the 1 km in 6 minutes and 4 seconds therefore her speed is $\frac{1}{6.06}$ kms per minute

Therefore Distance Covered by Saloni in 29.16 mins is 29.16 mins*$\frac{1}{6.06}$ $\approx$ 4.8 kms

Therefore the distance with which Sukriti will win a 5 km mini marathon is $\approx$ 200 meters

therefore our answer is option ‘B’

Average Speed of Car = $\frac{3250}{65}$ = 50 kmph
Average Speed of Bus =$\frac{3}{5}\times$ 50 = 30 kmph