aptitude formulas.docx

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1. km/hr to m/s conversion:

a km/hr = a x5

m/s.18

2. m/s to km/hr conversion:

a m/s = a x18

km/hr.5

3. Formulas for finding Speed, Time and Distance

4. Time taken by a train of length l metres to pass a pole or standing man or a signal post is

equal to the time taken by the train to cover l metres.

5. Time taken by a train of length l metres to pass a stationery object of length bmetres is the

time taken by the train to cover (l + b) metres.

6. Suppose two trains or two objects bodies are moving in the same direction at um/s and v m/s,

where u > v , then their relative speed is = (u - v ) m/s.

7. Suppose two trains or two objects bodies are moving in opposite directions at um/s and v m/s,then their relative speed is = (u + v ) m/s.

8. If two trains of length a metres and b metres are moving in opposite directions atu m/s

and v m/s, then:

The time taken by the trains to cross each other =(a + b)

sec.(u + v )

9. If two trains of length a metres and b metres are moving in the same direction atu m/s

and v m/s, then:

The time taken by the faster train to cross the slower train =

(a + b)

sec.(u - v )

10. If two trains (or bodies) start at the same time from points A and B towards each other and

after crossing they take a and b sec in reaching B and A respectively, then:

(A's speed) : (B's speed) = (b : a)

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length

of the train?

A. 120 metres B. 180 metres

C. 324 metres D. 150 metres

Answer & Explanation

http://www.indiabix.com/aptitude/time-and-distance/formulas





Answer: Option D

Explanation:

Speed= 60 x5

m/sec=

50

m/sec.18 3

Length of the train = (Speed x Time) =50

x 9m = 150 m.

3

View Answer Workspace Report Discuss in Forum

2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the

train is going, in 10 seconds. The speed of the train is:

A. 45 km/hr B. 50 km/hr

C. 54 km/hr D. 55 km/hr


Answer: Option B

Explanation:

Speed of the train relative to man =125

m/sec10

=25

m/sec.2

=25

x18

km/hr2 5

= 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = ( x - 5) km/hr.

x - 5 = 45 x = 50 km/hr.


3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can

cross in 30 seconds, is:

A. 200 m B. 225 m

C. 245 m D. 250 m


http://www.indiabix.com/aptitude/problems-on-trains/discussion-454










Answer: Option C

Explanation:

Speed = 45 x5

m/sec=

25

m/sec.18 2

Time = 30 sec.

Let the length of bridge be x metres.

Then,130 + x

=25

30 2

2(130 + x ) = 750

x = 245 m.


4. Two trains running in opposite directions cross a man standing on the platform in 27

seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio

of their speeds is:

A. 1 : 3 B. 3 : 2

C. 3 : 4 D. None of these


Answer: Option B

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27 x metres,

and length of the second train = 17y metres.

27 x + 17y = 23

x + y

27 x + 17y = 23 x + 23y

4 x = 6y







=3.

y 2View Answer Workspace Report Discuss in Forum

5. A train passes a station platform in 36 seconds and a man standing on the platform in

20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

A. 120 m B. 240 m

C. 300 m D. None of these


Answer: Option B

Explanation:

Speed = 54 x 5m/sec = 15 m/sec.

18

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then,+ 300

= 1536

x + 300 = 540

x = 240 m.

6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform

650 m long?

A. 65 sec B. 89 sec

C. 100 sec D. 150 sec


Answer: Option B

Explanation:

Speed =240

m/sec = 10 m/sec.24

Required time = 240 + 650







10View Answer Workspace Report Discuss in Forum

7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr

and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each

train is:

A. 50 m B. 72 m

C. 80 m D. 82 m


Answer: Option A

Explanation:

Let the length of each train be x metres.

Then, distance covered = 2 x metres.

Relative speed = (46 - 36) km/hr

= 10 x5

m/sec18

=25

m/sec9

2 x =

25

36 9

2 x = 100

x = 50.


8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge

140 m long?

A. 40 sec B. 42 sec

C. 45 sec D. 48 sec


Answer: Option A











Explanation:

Formula for converting from km/hr to m/s: X km/hr = X x5

m/s.18

Therefore, Speed = 45 x5

m/sec

=25

m/sec.

18 2

Total distance to be covered = (360 + 140) m = 500 m.

Formula for finding Time = Distance

Speed

Required time =500 x 2

sec= 40 sec.

25


9. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths

are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the

faster train in seconds is:

A. 36 B. 45

C. 48 D. 49


Answer: Option C

Explanation:

Relative speed = (60+ 90) km/hr

= 150 x5

m/sec18

=125

m/sec.3

Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.

Required time = 2000 x

3

sec = 48 sec.125


10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine

of a 120 metres long train running at 45 kmph in the same direction. In how much time

will the train pass the jogger?














A. 3.6 sec B. 18 sec

C. 36 sec D. 72 sec


Answer: Option C

Explanation:

Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.

= 36 x5

m/sec18

= 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.

Time taken =360

sec= 36 sec.

10

11. A 270 metres long train running at the speed of 120 kmph crosses another train running in

opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

A. 230 m B. 240 m

C. 260 m D. 320 m

E. None of these


Answer: Option A

Explanation:

Relative speed = (120 + 80) km/hr

= 200 x5

m/sec18

=500

m/sec.9

Let the length of the other train be x metres.



Then,+ 270

=500

9 9

x + 270 = 500

x = 230.


12. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds.

What is the length of the goods train?

A. 230 m B. 240 m

C. 260 m D. 270 m


Answer: Option D

Explanation:

Speed = 72 x5

m/sec= 20 m/sec.

18

Time = 26 sec.

Let the length of the train be x metres.

Then,+ 250

= 2026

x + 250 = 520

x = 270.


13. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one

is moving twice as fast the other, then the speed of the faster train is:

A. 30 km/hr B. 45 km/hr

C. 60 km/hr D. 75 km/hr












Answer: Option C

Explanation:

Let the speed of the slower train be x m/sec.

Then, speed of the faster train = 2 x m/sec.

Relative speed = ( x + 2 x ) m/sec = 3 x m/sec.

(100 + 100)= 3 x

8

24 x = 200

x =25

.3

So, speed of the faster train =50

m/sec3

=50

x18

km/hr3 5

= 60 km/hr.


14. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in

opposite directions on parallel tracks. The time (in seconds) which they take to cross each other,

is:

A. 9 B. 9.6

C. 10 D. 10.8


Answer: Option D

Explanation:

Relative speed = (60 + 40) km/hr = 100 x5

m/sec=

250

m/sec.18 9

Distance covered in crossing each other = (140 + 160) m = 300 m.

Required time = 300 x9

sec=

54sec = 10.8 sec.

250 5








15. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who

is running at 6 kmph in the direction opposite to that in which the train is going?

A. 5 sec B. 6 sec

C. 7 sec D. 10 sec


Answer: Option B

Explanation:

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

= 66 x 5

m/sec18

=55

m/sec.3

Time taken to pass the man = 110 x3

sec = 6 sec.55

16.

A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How

long does it take for the train to pass through the tunnel from the moment the front enters to the

moment the rear emerges?

A. 2.5 min B. 3 min

C. 3.2 min D. 3.5 min


Answer: Option B

Explanation:

Total distance covered =7

+1

miles2 4

=15

miles.4

Time taken = 15 hrs







4 x 75

=1

hrs20

=

1

x 60 min.20

= 3 min.


17. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then

the length of the tunnel (in meters) is:

A. 130 B. 360

C. 500 D. 540


Answer: Option C

Explanation:

Speed = 78 x5

m/sec =65

m/sec.18 3

Time = 1 minute = 60 seconds.

Let the length of the tunnel be x metres.

Then,800 + x

=65

60 3

3(800 + x ) = 3900

x = 500.


18. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18

seconds. What is the length of the platform?

A. 320 m B. 350 m

C. 650 m D. Data inadequate












Answer: Option B

Explanation:

Speed =300

m/sec =50

m/sec.18 3

Let the length of the platform be x metres.

Then,+ 300

=50

39 3

3( x + 300) = 1950

x = 350 m.


19. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

A. 50 m B. 150 m

C. 200 m D. Data inadequate


Answer: Option B

Explanation:

Let the length of the train be x metres and its speed by y m/sec.

Then, = 15 y = x

.y 15

+ 100=

x

25 15

15( x + 100) = 25 x

15 x + 1500 = 25 x

1500 = 10 x

x = 150 m.












20. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds

respectively. What is the speed of the train?

A. 69.5 km/hr B. 70 km/hr

C. 79 km/hr D. 79.2 km/hr


Answer: Option D

Explanation:

Let the length of the train be x metres and its speed by y m/sec.

Then, = 8 x = 8y y

Now,

+ 264

= y 20

8y + 264 = 20y

y = 22.

Speed = 22 m/sec = 22 x18

km/hr = 79.2 km/hr.5

1. Work from Days:

If A can do a piece of work in n days, then A's 1 day's work =1.

n

2. Days from Work:

If A's 1 day's work =1, then A can finish the work in n days.

n

3. Ratio:

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

1. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the

fraction of the work that is left is :



A.1

4B.

1

10

C.7

15D.

8

15


Answer: Option D

Explanation:

A's 1 day's work =1

;15

B's 1 day's work =1

;20

(A + B)'s 1 day's work =1

+1

=7

.15 20 60


x 4 =7

.60 15

Therefore, Remaining work = 1 -7

=8

.15 15


2. A can lay railway track between two given stations in 16 days and B can do the same job in 12

days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

A. 91

days5

B. 92

days5

C. 93

days5

D. 10


Answer: Option C

Explanation:

(A + B + C)'s 1 day's work =1

,4

A's 1 day's work =1

,16

B's 1 day's work =1

.12

C's 1 day's work =1

-1

+1

=1

-7

=5

.4 16 12 4 48 48

So, C alone can do the work in48

= 93

days.5 5


http://www.indiabix.com/aptitude/time-and-work/discussion-821










3. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do

the work if he is assisted by B and C on every third day?

A. 12 days B. 15 days

C. 16 days D. 18 days


Answer: Option B

Explanation:

A's 2 day's work =1

x 2 =1

.20 10

(A + B + C)'s 1 day's work =1

+1

+1

=6

=1

.20 30 60 60 10

Work done in 3 days =1

+1

=1.

10 10 5

Now,1

work is done in 3 days.5

Whole work will be done in (3 x 5) = 15 days.


4. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B.

Working together, they can do it in:

A. 20 days B. 221

days2

C. 25 days D. 30 days


Answer: Option B

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes3

x 60 = 90 days.2







So, A takes 30 days to do the work.

A's 1 day's work =1

30

B's 1 day's work =

1

90


+1

=4

=2

30 90 90 45

A and B together can do the work in45

= 221

days.2 2


5. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs.

3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A. Rs. 375 B. Rs. 400

C. Rs. 600 D. Rs. 800


Answer: Option B

Explanation:

C's 1 day's work =1

-1

+1

=1

-7

=1

.3 6 8 3 24 24

A's wages : B's wages : C's wages =

1

:

1

:

1

= 4 : 3 : 1.6 8 24

C's share (for 3 days) = Rs. 3 x1

x 3200 = Rs. 400.24





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