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5/25/13 Exam Reports

testfunda.com/LMS/Student/NewReports.aspx 1/13

1.1 Marks

A flight of Jet Airways from Delhi to Mumbai has an average speed of 700 kilometers per hour without any stoppage, whereas a flight ofKingfisher from Delhi to Mumbai has an average speed of 560 kilometers per hour with stoppage at Baroda. What is the average stoppagetime per hour of Kingfisher flight if both the planes fly at the same speed?

[FMS 2009]

1) 8 minutes

2) 12 minutes

3) 16 minutes

4) 24 minutes

Solution:Let the distance between Delhi and Mumbai be x km.

This means that the difference in the timing corresponds to the stoppage time.

If we want to find out the average stoppage time of the flight per hour, then we need to divide the total stoppage time by the actual timetaken to reach the destination.

This means that for every hour, the actual stoppage will be 1/5th of an hour, i.e. 12 minutes.

Hence, option 2.

Group Question

Answer the following questions based on the information given below.

Everyday Miss Yadav, Miss Sharma, Miss Toppo and Miss Hussain go to a park for morning walk. One day, they reach the gate of the park atthe same time and immediately start walking on the only circular track adjacent to the gate. Miss Yadav, Miss Toppo and Miss Hussain go on aclockwise direction while Miss Sharma goes anti-clockwise. Miss Hussain who is asthmatic is the slowest among the four and soon others moveaway from her. Like every day she could walk only one round taking almost the same time as others to complete their morning walk. After herwalk Miss Hussain reads the following instruction written at the gate while others join her one after another. Walkers are requested to use onlythe 500 m walking track. Plucking of flowers and leaves are strictly prohibited. The park will remain closed from 6 pm to 5 am.

While walking Miss Yadav overtakes Miss Hussain twice; once near the fountain and the other time at the signature rock. Miss Toppo and MissSharma cross her three times.

[FMS 2009]

2.1 Marks

What is the total distance covered by Miss Sharma and Miss Toppo together?

1) 3500 m

2) 4000 m

3) 2500 m

4) 3000 m

Solution:

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Solution:Miss Sharma is travelling in the opposite direction to Miss Hussain and crosses her on 3 occasions.

While Miss Hussain completes only 1 round, Miss Sharma will complete 3 rounds

Miss Sharma travels a distance of 500 3 = 1500 m

Now, Miss Toppo and Miss Hussain are travelling in the same direction.

Miss Toppo overtakes Miss Hussain thrice after meeting her in the beginning and before meeting her in the end of the walk.

Miss Toppo completes 4 rounds

Miss Toppo travels a distance of 500 4 = 2000 m

Miss Sharma and Miss Toppo together travel 3500 m

Hence, option 1.

3.1 Marks

How many times Miss Yadav and Miss Sharma cross each other on the track?

1) Twice

2) Three times

3) Four times

4) Five times

Solution:Miss Sharma and Miss Yadav both take 3 rounds across the park with approximately same speeds and travel in opposite directions.

They also start at the same time from the same point and end at the same point

They meet 2 times in every round.

They meet 6 times.

But the first time they meet is when they are just starting to walk.

They actually cross each other 5 times on the track.

Hence, option 4.

4.1 Marks

How many times Miss Toppo would overtake Miss Yadav?

1) Never

2) Once

3) Twice

4) Three times

Solution:Miss Toppo completes 4 rounds of the track (2000 m) and Miss Yadav completes 3 rounds of the track (1500 m).

They start walking at the same time and as Miss Toppo is walking faster than Miss Yadav, she is always ahead of her by somedistance which keeps increasing but they meet each other only after the end of their walk because by the time they finish their walksMiss Toppo gains a round (500 m) over Miss Yadav.

Miss Toppo will never overtake Miss Yadav

Hence, option 1.

5.1 Marks

Two men at points R and S, 76 kilometres apart, set out at the same time to walk towards each other. The man at R walks uniformly at the

rate of kilometres per hour; the man at S walks at the constant rate of kilometres per hour for the first hour, at kilometres per

hour for the second hour, and so on, in arithmetic progression. If the men meet x kilometres nearer R than S in an integral number of hours,then x is:

[FMS 2010]

1) 10

2) 8

3) 6

4) 4



4) 4

Solution:The two men meet when the sum of the distances covered by them is 76.

The men meet 36 km from R and 40 km from S.

They meet 4 km nearer to R than S.

Hence, option 4.

6.1 Marks

In a ten-kilometres race First beats Second by 2 kilometres and First beats Third by 4 kilometres. If the runners maintain constant speedsthroughout the race, by how many kilometres does Second beat Third?

[FMS 2010]

1)

2)

3)

4) 3

Solution:By the conditions given in the question we have that, if the first runs 10 km then the second runs 8 km and the third runs 6 km.

When the second runs 8 km the third runs 6 km.

The second beats the third by 2.5 km in a 10 km race.

Hence, option 2.

7.1 Marks A watch loses minutes per day. It is set right at 1 P.M. on March 15. Let n be the positive correction, in minutes, to be added to the

time shown by the watch at a given time. When the watch shows 9 A. M. on March 21, n equals :

[FMS 2010]

1)

2)

3)

4)



Solution:When the actual time elapsed is 24 hours = 24 60 = 1440 minutes,

the time elapsed on the faulty watch = 1437.5 minutes.

From 1 pm on March 15 to 9 am on March 21, the time elapsed on the faulty watch = 140 hours = 140 60 = 8400 minutes

Hence, option 1.

8.1 Marks

In racing over a given distance d at uniform speed, A can beat B by 20 metres, B can beat C by 10 metres, and A can beat C by 28 metres.Then d, in metres, equals :

[FMS 2010]

1) 58

2) 100

3) 116

4) 120

Solution:When A runs d metres, B runs (d 20) metres.

When B runs d metres, C runs (d 10) metres.

When A runs d metres, C runs (d 28) metres.

(d 20) (d 10) = d(d 28)

d2 30d + 200 = d2 28d

200 = 2d

d = 100 m

Hence, option 2.

9.1 Marks

A man drives 150 kilometres to the seashore in 3 hours and 20 minutes. He returns from the shore to the starting point in 4 hours and 10minutes. Let r be the average rate for the entire trip. Then the average rate for the trip going exceeds r, in kilometres per hour, by :

[FMS 2010]

1) 5

2)

3) 4

4) 2

Solution:



r = 40 km/hr

Average rate for the trip going exceeds r by 45 40 = 5 km/hr

Hence, option 1.

10.1 Marks

A man on his way to dinner shortly after 6:00 p.m. observes that the hands of his watch form an angle of 110. Returning before 7:00 p.m.he notices that again the hands of his watch form an angle of 110. The number of minutes that he has been away is :

[FMS 2010]

1)

2) 40

3) 42

4) 42.4

Solution:When the hour hand and minute hand form an angle of 110, x minutes after 6:00 pm, we have two possibilities

1. The minute hand is behind the hour hand.

The speed of the minute hand is 6 per minute and the speed of the hour hand is 0.5 per minute.

Initial distance between the hour and the minute hands at 6:00 pm is 180

(180 + 0.5x) (6x) = 110

180 5.5x = 110

x 12.72 minutes 12 minutes 43 seconds.

2. The minute hand is ahead of the hour hand.

6x 180 0.5x = 110

5.5x 180 = 110

x 52.72 minutes 52 minutes 43 seconds

The man leaves at 06:12:43 pm and returns at 06:52:43 pm

He is away for 40 minutes.

Hence option 2.

11.1 Marks

A train, an hour after starting, meets with an accident which detains it for a half hour, after which it proceeds at 3/4 of its former rate andarrives 3(1/2) hours late. Had the accident happened 90 kilometers farther along the line, it would have arrived only 3 hour late. The length ofthe trip in kilometers was:

[FMS 2011]

1) 400

2) 465

3) 600

4) 640

Solution:Let the train travel at s km/hr.

In 1 hour it travels s km.



In 1 hour it travels s km.

Let the remaining distance be x km. Then,

x = 9s

Total distance = s + x = 10s

Using the second condition,

s = 60

Total distance = 60 10 = 600 km.

Hence, option 3.

12.1 Marks

The times between 7 and 8 oclock, correct to the nearest minute, when the hands of a clock will form an angle of 84 degrees are:

[FMS 2011]

1) 7: 23 and 7: 53

2) 7: 20 and 7: 50

3) 7: 22 and 7: 53

4) 7: 23 and 7: 52

Solution:At 7O clock the angle between the hour and minute hand = 210 (in clockwise direction)

Relative speed of minute hand & hour hand = 5.5 degrees/minute.

The angle between the two hands is 84 in two cases

(i) The minute hand travels a distance of 210 84 = 126

(ii) The minute hand gains 84 over the hour hand i.e. it travels 210 + 84 = 294

Hence, option 1.

13.1 Marks

Hari and Ravi started a race from opposite ends of the pool. After a minute and a half, they passed each other in the center of the pool. Ifthey lost no time in turning and maintained their respective speeds, how many minutes after starting did they pass each other the secondtime?

1) 3

2)

3) 6

4)



4)

Solution:As the two met in the centre of the pool, their speeds must be equal and both of them cover a distance equal to half the length of the pool in1.5 minutes.

In the first 1.5 minutes, Hari travels from A to B and Ravi from C to B.

In the second 1.5 minutes, Hari travels from B to C and Ravi from B to A.

In the third 1.5 minutes Hari travels from C to B and Ravi from A to B.

They passed each other the second time 4.5 minutes after starting.

Hence, option 2.

14.1 Marks

Two boys A and B start at the same time to ride from Delhi to Meerut, 60 kilometers away. A travels 4 kilometers an hour slower than B. B

reaches Meerut and at once turns back meeting A 12 kilometers from Meerut. The rate of A was:

[FMS 2011]

1) 4 kph

2) 8 kph

3) 12 kph

4) 16 kph

Solution:

Before meeting A, B travels 60 + 12 = 72 km

And A travels 60 12 = 48 km

Let Vb be the speed of B and Va be speed of A.

Now Vb = Va + 4

2Va + 8 = 3Va

Va = 8

Hence, option 2.

15.1 Marks

Two cyclist, k kilometres apart, and starting at the same time, would be together in r hours if they travelled in the same direction, but wouldpass each other in t hours if they travelled in opposite direction. The ratio of the speed of the faster cyclist to that of the slower is:

[FMS 2011]

1)

2)

3)

4)



Solution:Let the speed of the faster and slower cyclist be a and b respectively.

By given conditions,

ar rb = at + tb

Hence, option 1.

16.1 Marks

The Ghaziabad-Hapur-Meerut EMU and the Meerut-Hapur-Ghaziabad EMU start at the same time from Ghaziabad and Meerut and proceedtowards each other at 16 km/hr and 21 km/hr, respectively. When they meet, it is found that one train has travelled 60 km more than theother. The distance between two stations is:

[IIFT 2007]

1) 445 km

2) 444 km

3) 440 km

4) 450 km

Solution:Let the distance covered by the slower train (i.e. the 16 km/hr one) be x km. Then, the distance covered by the faster train will be (x + 60)km.Since the two trains start simultaneously and both stop when they meet each other, the time of travel of both trains is equal.

Hence, Distance Speed

The total distance = x + x + 60 = 2 192 + 60 = 444

Hence, option 2.

17.1 Marks

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Thespeed of the boat in still water is:

[IIFT 2008]

1) 3 km/hour

2) 4 km/hour

3) 8 km/hour

4) None of the above

Solution:Let the time taken to go of 30 km upstream be 3x hours. Then the time taken to go 40 km upstream is 4x hours.

Let the time taken to go 44 km downstream be 4y hours. Then the time taken to go 55 km downstream is 5y hours.

Then we have:

3x + 4y = 10 (i)



4x + 5y = 13 (ii)

Solving for x and y, we have,

x = 2 and y = 1

Hence, option 3.

18.1 Marks

Two motorists Anil and Sunil are practicing with two different sports cars: Ferrari and Maclarun, on the circular racing track, for the carracing tournament to be held next month. Both Anil and Sunil start from the same point on the circular track .Anil completes one round ofthe track in 1 minute and Sunil takes 2 minutes to compete a round. While Anil maintains same speed for all the rounds, Sunil halves his

speed after the completion of each round. How many times Anil and Sunil will meet between the 6th round and 9th round of Sunil (6th and 9th

round is excluded)? Assume that the speed of Sunil remains steady throughout each round and changes only after the completion of thatround.

[IIFT 2009]

1) 260

2) 347

3) 382

4) None of the above

Solution:Anil and Sunil meet every time Anil gains a round over Sunil.

When Sunil completes one round of the track of length, say d, in 2 minutes, Anil meets Sunil every

Anil meets Sunil 2/2 = 1 time in his first round.

When Sunil completes one round of the track of length, say d, in 2n minutes, Anil meets Sunil every

Anil meets Sunil 27 1 = 127 times in the 7th round and 28 1 = 255 times in the 8th round.

They will meet 127 + 255 = 382 times between the 6th and 9th rounds.

Hence, option 3.

19.1 Marks

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 6minutes 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:

[IIFT 2009]

1) 150 m

2) 200 m

3) 175 m

4) 225 m



Solution:Sukriti runs 1 km in 5 minutes and 50 seconds = 350 seconds.

Saloni runs 1 km in 6 minutes and 4 seconds = 364 seconds.

Sukriti runs 5 km in 5 350 = 1750 seconds

Sukriti will win the mini marathon by 5 4.8 = 0.2 km = 200 m

Hence, option 2.

20.1 Marks

Mukesh, Suresh and Dinesh travel from Delhi to Mathura to attend Janmasthmi Utsav. They have a bike which can carry only two riders at atime as per traffic rules. Bike can be driven only by Mukesh. Mathura is 300Km from Delhi. All of them can walk at 15Km/Hrs. All of themstart their journey from Delhi simultaneously and are required to reach Mathura at the same time. If the speed of bike is 60Km/Hrs thenwhat is the shortest possible time in which all three can reach Mathura at the same time.

[IIFT 2010]

1)

2)

3) 10 Hrs

4) None of these

Solution:

Let Mukesh take Suresh on his bike till B and leave him there to walk till C(Mathura). In the meanwhile, Dinesh keeps walking to reach D,Mukesh comes back picks Dinesh and then both ride to Mathura.

When Mukesh comes back, let us say he meets Dinesh at E.

Let AB = x, then BC = 300 x

Since Dinesh walks at 15 kmph and bikes speed is 60 kmph, we have AD = x/4.

4(300 x) = 300 + x/5



Hence, minimum time

Hence, option 2.

21.1 Marks

Mandeep and Jagdeep had gone to visit Ranpur, which is a seaside town and also known for the presence of the historical ruins of anancient kingdom. They stayed in a hotel which is exactly 250 meters away from the railway station. At the hotel, Mandeep and Jagdeeplearnt from a tourist information booklet that the distance between the sea-beach and the gate of the historical ruins is exactly 1 km. Nextmorning they visited the sea-beach to witness sunrise and afterwards decided to have a race from the beach to the gate of the ruins.Jagdeep defeated Mandeep in the race by 60 meters or 12 seconds. The following morning they had another round of race from the railwaystation to the hotel. How long did Jagdeep take to cover the distance on the second day?

[IIFT 2011]

1) 53 seconds

2) 47 seconds

3) 51 seconds

4) 45 seconds

Solution:Jagdeep defeated Mandeep in a 1000 m race by 60 m or 12 s.This means that Mandeep would travel 60 m in 12 s. Mandeeps speed = 5 m/s Mandeep covered 1000 m in 1000/5 = 200 s Jagdeep covered 1000 m in 200 12 = 188 s Jagdeep covered 250 m in 47 s.Hence, option 2.

22.1 Marks

Four people Ahmed, Burman, Chhaya, and Deepak in that order occupy the four corners of a square of side a in clockwise order. Ahmedand Burman simultaneously start walking at the same speed towards Burman and Chhaya respectively. Both of them stop walking whenBurman reaches Chhaya. What is the distance between Ahmed and Burman?

[JMET 2008]

1) a

2) 0

3)

4)

Solution:Ahmed walks towards Burman and Burman walks towards Chhaya. Burman walks along the side of the square, but Ahmed walks a curvedpath. As the shortest distance between Ahmeds initial position and Chhayas position is a2, Ahmeds path is of length greater than a2.

When Burman reaches Chhaya, he has travelled a distance of a units and so has Ahmed.

Distance between Ahmed and Burman = Length of Ahmeds path a

Hence, option 4.



Group Question

Answer the following questions based on the information given below.

Consider a circular running track of radius "r". Two runners Anand and Ben are on the running track at a distance of " r" from each other. Theyalways run in a clockwise direction. The running track is such that the runners lose energy on one contiguous half of the track and gain energy inthe other contiguous half of the track. Let both Anand and Ben have initial energy levels of "E".

[JMET 2010]

23.1 Marks

Let the runners consume or gain unit energy per unit distance traveled. Also, let the energy consumed or gained be independent ofthe distance traveled thus far when the energy levels are greater than zero. The runners come to a stop when all their energy isexpended. Assuming that both runners run at the same constant speed "s". After traveling a distance of 2nr where n is a non-negative integer, what is the difference in energy levels of Anand and Ben?

1) 0

2) r

3) nr

4) nrs

Solution:Let Anand and Ben be standing at the positions shown.

The runners gain or lose unit energy per unit distance travelled.

Energy gained by Anand when he completes each full circle of length 2r is

r r = 0

Similarly, energy gained by Ben = r + r = 0

Difference in energy levels of Anand and Ben after completing each round of distance 2r is 0.

Difference in energy levels of Anand and Ben after travelling a distance of 2nr = 0

Hence, option 1.

24.1 Marks

Assume that the position of Anand on the track is chosen randomly and Ben is at a distance of r from Anand. What could havebeen the maximum possible difference in the energy levels between them during the process of completing one full circle?

1) 0

2) r

3) 2r

4)

Solution:Assuming that the runners gain or lose unit energy per unit distance travelled, the maximum possible difference in their energies willbe when Anand has gained r units of energy and Ben has lost r units of energy.

The maximum difference = (E + r) (E r) = 2r

Hence, option 3.

25.1 Marks

Anand is at the start of the half circle that boosts energy and Ben at the start of the half circle that dissipates energy. Now, if theenergy lost or gained per unit distance is proportional to the distance traveled thus far, with "k " being the energy lost or gained perunit distance travelled, what is the difference in the energy levels when Anand reaches the position of Ben and vice-versa?

1) 2kr



2) k2r2

3) k2r2/2

4) kr/2

Solution:When Anand reached Bens position, he has gained rk units of energy.When Ben reaches Anands position, he has lost rk units of energy. Difference = (E + rk ) (E rk ) = 2rk Hence, option 1.

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