Directly Proportional

Q.

Three numbers are in the ratio 1 : 2 : 3 and their H.C.F. is 12. Which of the following correctly denotes the numbers?

1. 10, 20, 30

2. 4, 8, 12

3. 5, 10, 15

4. 6, 12, 18

5. 12, 24, 36

Q.

Walking ${\frac{6}{7}}^{\mathrm{th}}$ of his usual speed, a man is $12\mathrm{minutes}$ too late. What is the usual time taken by him to cover that distance?

Q. Two trains start at the same time from A and B and proceed towards B and A at 36 km/h and 42 km/h, respectively. When they meet, it is found that one train has moved 48 km more than the other. Then, the distance between A and B (in km) is:

1. 460
2. 544
3. 636
4. 624

Q.

The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?

1. 36

2. 18

3. 20

4. 27

Q. With an average speed of 40 Km/h, a train reaches its destination on time. If it goes with an average speed of 35 Km/h, it reaches late by 15 minutes. The total journey is of :

1. 30 Km
2. 40 Km
3. 70 Km
4. 80 Km

Q.

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?

1. 230 m

2. 240 m

3. 340 m

4. 320 m

5. 260 m

Q. The L.C.M. of two numbers is 495 and their H.C.F. is 5. If the sum of the two numbers is 100 then their difference is _____.

1. 28
2. 46
3. 10
4. 70
5. 90

Q. Three friends A, B and C start running around a circular stadium and complete a single round in 24 seconds, 36 seconds and 30 seconds respectively. After how many minutes will they meet again at the starting point?

1. 6
2. 12
3. 8
4. 15
5. 55

Q. The L.C.M. and H.C.F of two numbers x and y are 3 and 105 respectively. If $x+y=36$, the value of $\frac{1}{x}+\frac{1}{y}$ is ___.

1. None of these
2. 1
3. $\frac{1}{6}$
4. $\frac{12}{315}$
5. $\frac{4}{35}$

Q.

Two trains are running at 40 kmph and 20 kmph respectively in the same direction. Faster train completely passes a man sitting in the slower train in 5 seconds. What is the length of the faster train?

1. 23 m

2. 27 m

3. 28 m

4. 209/9 m

5. 250/9 m

Q. In a 10 km race, A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C? ___

Q.

How many seconds will a 500 metre long train take to cross a man walking at a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

1. 40

2. 45

3. 55

4. 25

5. 30

Q.

A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. What is the speed of the train?

1. 50 km/hr

2. 54 km/hr

3. 55 km/hr

4. 60 km/hr

5. 45 km/hr

Q. An aeroplane travels 2500 Km, 1200 Km and 500 Km at 500 Km/h, 400 Km, and 250 Km/h, respectively.
The average speed is:

1. 405 Km/h
2. 575 Km/h
3. None of these
4. 420 Km/h
5. 410 Km/h

Q.

Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in kmph) is:

1. 72

2. 80

3. 18

4. 30

5. 36

Q. Pankaj went to the post-office at the speed of 60 km/hr. While returning to his home, he covered half of the distance at the speed of 10 km/hr, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest half of the distance at the speed of 30 km/hr. The average speed of the Pankaj in the whole length of journey is :

1. 22.88 km/hr
2. 5.45 km/hr
3. 5.67 km/hr
4. 24 km/hr

Q.

The distance between Bholu’s and Golu’s house is$9$ km. Bholu has to attend Golu’s birthday party at $7$o’clock. He started from his home at $6$ o’clock on his bicycle and covered a distance of$6$ km in$40$ minutes. At that point, he met Chintu and he spoke to him for $5$minutes and reached Golu’s birthday party at $7$o’clock. With what speed did he cover the second part of the journey? Calculate his average speed for the entire journey. The speed with which Bholu covered the second part of the journey

Q. The average speed of a train running at a speed of 30 Km/h during the first 100 kilometres, at 40 Km/h during the second 100 kilometres and at 50 Km/h during the last 100 kilometres is nearly:

1. 39.2 Km/h
2. None of these
3. 38.3 Km/h
4. 40.0 Km/h
5. 38.5 Km/h

Q. Three runners A, B and C run a race, with runner A finishing 12 meters ahead of runner B and 18 meters ahead of runner C, while runner B finishes 8 meters ahead of runner C. Each runner travels the entire distance at a constant speed. What was the length of the race? (2001)

1. 36 meters
2. 72 meters
3. 48 meters
4. 60 meters

Q. Two people started simultaneously from points A and B towards each other. At the moment the person who started from A had covered two-thirds of the way, the other person had covered 2 km less than half the total distance. If it is known that when the person who started from B had covered $\frac{1}{4}$ of the way, the other person was 3 km short of the midpoint. Find the distance between A and B. The speeds of the two people were constant.

1. $Both\left(aandb\right)$
2. $3\sqrt{17}-5km$
3. $(15+3\sqrt{17})km$
4. $(15-3\sqrt{17})km$

Q.

Two trains having length of 280 m and 320 m long run at the speed of 120 kmph and 80 kmph respectively in opposite directions (on parallel tracks). What is the time which they will take to cross each other?

1. 10.8 secs

2. 8.8 secs

3. 12.8 secs

4. 11.2 secs

5. None of these

Q. A train overtakes two girls who are walking in the opposite direction in which the train is going at the rate of 3 km/h and 6 km/h and passes them completely in 36 seconds and 30 seconds respectively. The length of the train (in metres) is:

1. 125 m
2. 120 m
3. 150 m
4. None of these

Q.

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively.
What is the time taken by the faster train to cross the slower train (in seconds)?

1. 48

2. 36

3. 45

4. 54

5. 49

Q. Two trains started running from the same point at the same time in opposite directions(one towards the North and other towards the South).The speed of the two trains is 22 m/s and 8 m/s respectively. How much time will they take to be 378 km apart?

1. 3 h 45 min
2. 3 h 20 min
3. 3 h 30 min
4. 4 h 30 min
5. 2 h 15 min

Q.

The wheel of a motor cycle is of radius $35\text{cm}$ . How many revolutions per minute must the wheel make so as to keep a speed of $66\text{km/h}$

Q. Anil and Sunil can complete a job in 15 days and 20 days respectively. Both of them started it together. Anil left 6 days before the work was completed. Find the time taken (in days) to complete the work.

1. 8
2. 10
3. 12
4. 14

Q.

A bus travels the first one-fourth of a certain distance with a speed of 20 km/hr, the next one-fourth distance with a speed of 40 km/hr, and the last one-half distance with a speed of 120 km/hr. What is the average speed of the bus for the whole journey?

1. None of these

2. 43 (7/11)kmph

3. 45 (5/11) kmph

4. 40 (10/11) kmph

5. 36 (4/11) kmph

Q.

A man walks $4\frac{1}{3}$ $km$ in one $hour$ . What distance will he walk in $2\frac{1}{3}$ hours?

Q. Shaurya and Arjit take a straight route to the same terminal point and travel with constant speeds. At the initial moment, the positions of the two and the terminal point form an equilateral triangle. When Arjit covered a distance of 80 km, the triangle becomes right-angled. When Arjit was at a distance of 120 km from the terminal point, the Shaurya arrived at the point. Find the distance between them at the initial moment assuming that there are integral distances throughout the movements described.

1. 300 km
2. 240 km
3. 225 km
4. 200 km

Q. Two riders on the horseback with a gun and a bullet proof shield were moving towards each other at a constant speed of 20km/h and 5km/h respectively. When they were 100 km apart, they started firing bullets at each other at the speed of 10km/h. When a bullet of rider 1 hits the shield of rider 2, rider 2 fires a bullet and the process continue vice versa. Neglecting the time lag at the instant when the bullet hits the shield and the rider fires the shot, find the total distance covered by all the bullets shot by both the riders.

1. 50 km
2. 40 km
3. 6 km
4. 60 km