SOLVED MATHEMATICS QUESTIONS

Trains and Work

1. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?

A. Insufficient data          B. 3 : 1

C. 1 : 3                             D. 3 : 2

2.  A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?

A. 46      B. 36

C. 18      D. 22

3.  A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is

A. None of these             B. 280 meter

C. 240 meter      D. 200 meter

4.  Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is

A. 2 : 3   B. 2 :1

C. 4 : 3   D. 3 : 2

5. A train having a length of 1/4 mile , is traveling at a speed of 75 mph. It enters a tunnel 3 ½ miles long. How long does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

A. 3 min                B. 4.2 min

C. 3.4 min            D. 5.5 min

6. A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?

A. 62 m B. 54 m

C. 50 m D. 55 m

7. Two trains, each 100 m long are moving in opposite directions. They cross each other in 8 seconds. If one is moving twice as fast the other, the speed of the faster train is

A. 75 km/hr        B. 60 km/hr

C. 35 km/hr         D. 70 km/hr

8. Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?

A. 10.30 a.m       B. 10 a.m.

C. 9.10 a.m.         D. 11 a.m.

9.  A train 108 m long is moving at a speed of 50 km/hr . It crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train?

A. 82 kmph         B. 76 kmph

C. 44 kmph          D. 58 kmph

10.  32. Two trains are approaching each other with the speed of 25km/hr. and 30km/hr. respectively from two different stations A and B. When two trains will meet each other, the second train had covered 20 km more than the first train. What is the distance between A and B stations?

A. 220 km                                                                        B. 200km

C. 440 km                                                                         D. 100 km

               

11. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

A. 8/15                  B. 7/15

C. 11/15                D. 2/11

12. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?

A. 9(3/5) days    B. 9(1/5) days

C. 9(2/5) days    D. 10 days

13. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?

A. 10 days            B. 14 days

C. 15 days            D. 9 days

14.  A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.

A. 18 days            B. 22 ½ days

C. 24 days            D. 26 days

15. A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?

A. Rs. 380             B. Rs. 600

C. Rs. 420             D. Rs. 400

16. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.

A. 4 days              B. 6 days

C. 2 days              D. 8 days

17. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

A. 37 ½ days       B. 22 days

C. 31 days            D. 22 days

18. P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?

A. 9        B. 11

C. 13      D. 15

19. If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.

A. 12      B. 14

C. 16      D. 18

20. There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?

A. 3 1⁄4 days       B. 4 1⁄3 days

C. 5 1⁄6 days       D. 6 1⁄5 days

Answers

1.        Answer : Option D

Explanation :

Let the speed of the trains be x and y respectively

length of train1 = 27x

length of train2 = 17y

Relative speed= x+ y

Time taken to cross each other = 23 s

=> (27x + 17 y)/(x+y) = 23

=> (27x + 17 y)/ = 23(x+y)

=> 4x = 6y

=> x/y = 6/4 = 3/2

2.        Answer : Option B

Explanation :

Distance to be covered = 240+ 120 = 360 m

Relative speed = 36 km/hr = 36×10/36 = 10 m/s

Time = distance/speed = 360/10 = 36 seconds

3.         Answer : Option C

Explanation :

Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s

Length of the train = speed × time taken to cross the man = 15×20 = 300 m

Let the length of the platform = L

Time taken to cross the platform = (300+L)/15

=> (300+L)/15 = 36

=> 300+L = 15×36 = 540

=> L = 540-300 = 240 meter

4.        Answer : Option C

Explanation :

Ratio of their speeds = Speed of first train : Speed of second train

= √16−−√9

= 4:3

5.        Answer : Option A

Explanation :

Total distance = 3 ½ + ¼ = 7/2 + ¼ = 15/4 miles

Speed = 75 mph

Time = distance/speed = (15/4) / 75 hr = 1/20 hr = 60/20 minutes = 3 minutes

6.        Answer : Option C

Explanation :

Let x is the length of the train in meter and v is its speed in kmph

x/9 = ( v-2)(10/36) ---(1)

x/10 =( v-4) (10/36) --- (2)

Dividing equation 1 with equation 2

10/9 = (v-2)/(v-4)

=> 10v - 40 = 9v - 18

=> v = 22

Substituting in equation 1, x/9 = 200/36 => x = 9×200/36 = 50 m

7.        Answer : Option B

Explanation :

Total distance covered = 100+100 = 200 m

Time = 8 s

let speed of slower train is v . Then the speed of the faster train is 2v

(Since one is moving twice as fast the other)

Relative speed = v + 2v = 3v

3v = 200/8 m/s = 25 m/s

=> v = 25/3 m/s

Speed of the faster train = 2v = 50/3 m/s = (50/3)×(36/10) km/hr

=> 5×36/3 = 5×12 = 60 km/hr

8.        Answer : Option B

Explanation :

Assume both trains meet after x hours after 7 am

Distance covered by train starting from P in x hours = 20x km

Distance covered by train starting from Q in (x-1) hours = 25(x-1)

Total distance = 110

=> 20x + 25(x-1) = 110

=> 45x = 135

=> x= 3

Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

9.        Answer : Option A

Explanation :

Total distance = 108+112 = 220 m

Time = 6s

Relative speed = distance/time = 220/6 m/s = 110/3 m/s

= (110/3) × (18/5) km/hr = 132 km/hr

=> 50 + speed of second train = 132 km/hr

=> Speed of second train = 132-50 = 82 km/hr

10.    Answer : Option A

Explanation :

Relative Difference : Distance1 - Distance2 = 20 km

Speed1 - Speed2 = 5km/hr

So, Time = Distance/Speed

= 20km/5

Time = 4 hrs.

Now, Distance is equal to Speed x Time.

(30km/hr + 25km/hr)x4

= 55x4

Ans = 220 km.

Or

Let the distance traveled by the first train and second train be x and (x+20) respectively.

Since time taken by both trains are same when they meet each other,

x/25 = (x+20)/30

x/5 = (x+20)/6

6x = 5x + 100

x = 100

Distance between A and B = x + (x+20) = 220 km

11.    Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15

12. Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/16

Amount of work Q can do in 1 day = 1/12

Amount of work P, Q and R can together do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence R can do the job on 48/5 days = 9 (3/5) days

12.    Answer : Option C

Explanation :

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days

13.    Answer : Option B

Explanation :

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 22 ½ days

14.    Answer : Option D

Explanation :

Amount of work A can do in 1 day = 1/6

Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day

= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400

15.    Answer : Option A

Explanation :

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8b = 1/10

=> 60m + 80b = 1 --- (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48b = ½

=> 52m + 96b = 1--- (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days

16.    Answer : Option A

Explanation :

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 ---(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 ½ days

17.    Answer : Option C

Explanation :

Work done by P in 1 day = 1/23

Let work done by Q in 1 day = q

q × (130/100) = 1/23

=> q = 100/(23×130) = 10/(23×13)

Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13

=> P and Q together can do the work in 13 days

18.    Answer : Option B

Explanation :

Work done by P in 1 day = 1/24

Work done by Q in 1 day = 1/6

Work done by R in 1 day = 1/12

Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24

=> Working together, they will complete the work in 24/7 days = 3 3⁄7 days

19.    Answer : Option C

Explanation :

Wages of 1 woman for 1 day = 21600/40×30

Wages of 1 man for 1 day = 21600×2/40×30

Wages of 1 man for 25 days = 21600×2×25/40×30

Number of men = 14400/(21600×2×25/40×30)=144/(216×50/40×30)=144/9=16

20.    Answer : Option C

Explanation :

Work completed in 1st day = 1/16

Work completed in 2nd day = (1/16) + (1/16) = 2/16

Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16

An easy way to attack such problems is from the choices. You can see the choices are  very close to each other. So just see one by one.

For instance, The first choice given in 3 1⁄4

The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16

The work done in 4 days = (1+2+3+4)/16 = 10/16

The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?

The work done in 6 days = (1+2+3+4+5+6)/16 > 1

Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.

(Just for your reference, work done in 5 days = 15/16.

Pending work in 6th day = 1 – 15/16 = 1/16.

In 6th day, 6 people are working and work done = 6/16.

To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.

Hence total time required = 5 + 1/6 = 5 1⁄6 days