Question 1

A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey ?

Accepted Answer

Speed of Man = 4.5 kmph Speed of stream = 1.5 kmph Speed in DownStream = 6 kmph Speed in UpStream = 3 kmph Average Speed = (2 x 6 x 3)/9 = 4 kmph.

Question 2

A bus covers its journey at the speed of 80km/hr in 10hours. If the same distance is to be covered in 4 hours, by how much the speed of bus will have to increase ?

Accepted Answer

Initial speed = 80km/hr Total distance = 80 x 10 = 800km New speed = 800/4 =200km/hr Increase in speed = 200 - 80 = 120km/hr

Question 3

In what time a 360 m. long train moving at the speed of 44 km/hr will cross a 140 m. long bridge ?

Accepted Answer

Speed = 44 kmph x 5/18 = 110/9 m/s We know that, Time = distance/speed Time = (360 + 140) / (110/9) = 500 x 9/110 = 41 sec.

Question 4

K and L starts walking towards each other at 4 pm at speed of 3 km/hr and 4 km/hr respectively. They were initially 17.5 km apart. At what time do they meet ?

Accepted Answer

Suppose they meet after 'h' hours Then 3h + 4h = 17.5 7h = 17.5 h = 2.5 hours So they meet at => 4 + 2.5 = 6:30 pm

Question 5

Mr. Karthik drives to work at an average speed of 48 km/hr. Time taken to cover the first 60% of the distance is 20 minutes more than the time taken to cover the remaining distance. Then how far is his office ?

Accepted Answer

Let the total distance be 'x' km. Time taken to cover remaining 40% of x distance is t 1 = 40 × x 100 × 48 But given time taken to cover first 60% of x distance is t 2 = t 1 + 20 60 h r s t 2 = 60 × x 100 × 48 ∴ 60 × x 100 × 48 = 40 × x 100 × 48 + 20 60 x=80 km.

Question 6

A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is

Accepted Answer

Let distance = x km and usual rate = y kmph. Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i) Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii) On dividing (i) by (ii), we get: x = 40 km.

Question 7

Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes?

Accepted Answer

Let p be the speed of man in kmph According to the given data in the question, Distance travelled by bus in 10 min with 20 kmph == Distance travelled by man in 8 min with (20 + p) kmph in opposite direction => 20 x 10/60 = 8/60 (20 + p) => 200 = 160 + 8p => p = 40/8 = 5 kmph.

Question 8

The ratio of the speeds of a car, a jeeps and a tractor is 3 : 5 : 2. The speed of the jeep is 250 per cent of the speed of the tractor and tractor covers 360 km in 12 hours. What is the average speed of car and jeep together?

Accepted Answer

Speed of tractor = 360/12 = 30 kmph Speed of jeep = 250 x 30/100 = 75 kmph But, given ratio of speed of car, jeep and tractor is 3 : 5 : 2 Speed of car = 3 x 75/5 = 45 kmph Required, average speed of car and jeep = 75 + 45/2 = 60 kmph.

Question 9

A man travels 480 km in 4 hours, partly by air and partly by train. If he had travelled all the way by air, he would have saved 4/5 of the time he would have taken to travel by train and would have arrived at his destination 2 hours early. Find the …

Accepted Answer

120 km

Question 10

A person goes to his office at 1/3rd of the speed at which he returns from his office. If the average speed during the whole trip is 12 m /h . what is the speed of the person while he was going to his office?

Accepted Answer

u = k , v= 3k ∴ 2 u v u + v ⇒ 2 × k × 3 k k + 3 k = 12 => k = 8km/h

Question 11

Den Bosch and Eastbourne are two famous cities 300 km apart. Maradona starts from Den Bosch at 8:24 am . An hour later pele starts from Den Bosch. After travelling for 1 hour , Pele reaches Nottingham that Maradona had passed 40 minutes earlier. Not…

Accepted Answer

Let Pele x km in 1 hour. so Maradona takes (2h-40min)=1 h 20 min to cover x km. Let speed of Maradona and Pele be M and P respectively than x =M x (4/3) and x= P x 1 => M/P = 3/4 Again 300 M = 300 P = 1 ⇒ 300 3 k - 300 4 k = 1 => k= 25 M= 3k = 75 km/h and P= 4k = 100 km/h ( Through options it is very easy to solve)

Question 12

In a daily morning walk three persons step off together. their steps measure 75 cm, 80 cm and 85 cm respectively. What is the minimum distance each should walk so that thay can cover the distance in complete steps ?

Accepted Answer

To find the minimum distance, we have to get the LCM of 75, 80, 85 Now, LCM of 75, 80, 85 = 5 x 15 x 16 x 17 = 20400 Hence, the minimum distance each should walk so that thay can cover the distance in complete steps = 20400 cms = 20400/100 = 204 mts.

Question 13

A man walks 6 km at a speed of 112 kmph, runs 8 km at a speed of 2 kmph and goes by bus another 32 km. Speed of the bus is 8 kmph. Find the average speed of the man in kmph. A) 4314 B) 4213 C) 2413 D) 3414

Accepted Answer

Man walked 6 km at 1.5 kmph, again he walked 8 km at speed of 2 kmph and 40 km at a speed of 8kmph time taken indivisually: => 6/1.5 = 4 m => 8/2 = 4 m => 40/8 = 5 m Average speed of man= total distance/ total time => 54/13 = 4 2 13 kmph

Question 14

A bike runs at the speed of 35 km/h when not serviced and runs at 55 km/h, when serviced. After servicing the bike covers a certain distance in 5 h. How much approximate time will the bike take to cover the same distance when not serviced?

Accepted Answer

Given speed of the bike after servicing = 55 kmph Time taken for travelling some distance at 55 kmph = 5 hrs Then, Distance = Speed x Time = 55 x 5 = 275 kms. Now, Speed of the bike before servicing = 35 kmph Distance = 275 kms Now, Time = Distance/Speed = 275/35 = 7.85 hrs =~ 8 hrs.

Question 15

The respective ratio between the speed of a bike, a van and lorry is 3 : 5 : 2. The speed of the van is 250 percent of the speed of the lorry which covers 360 km in 12 hours. What is the average speed of the bike and the van together?

Accepted Answer

Speed of lorry = 360 12 = 30 kmph Speed of van = 250 100 x 30 = 75 kmph Speed of bike = 3 5 x 75 = 45 kmph Therefore, now required average speed of bike and van = 75 + 45 2 = 60 kmph.

Question 16

Two trains 85 m and 75 m long are running in same direction with speeds of 62 km/hr and 44 km/hr respectively. In what time will the first train cross the second train ?

Accepted Answer

Given that, 1st train speed = 62 km/hr 2nd train speed = 44 km/hr Hence the relative speed of two trains is : 62-44 = 18 km/hr = 18 × 5 18 m/s = 5 m/s. There fore, the first train crosses the second train i.e (85+75)mts of distance with a speed of 5m/s in, time = d i s tan c e s p e e d = 85 + 75 5 = 32 sec.

Question 17

Two trains start from same place at same time at right angles to each other. Their speeds are 36km/hr and 48km/hr respectively. After 30 seconds the distance between them will be ?

Accepted Answer

Using pythagarous theorem, distance travelled by first train = 36x5/18x30 = 300m distance travelled by second train = 48x5/18x30 = 400m so distance between them =√( 90000 + 160000) = √250000 = 500mts.

Question 18

P is faster than Q. P and Q each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, P's speed is equal to ?

Accepted Answer

Let P's speed = x km/hr. Then, Q's speed = (7 - x) km/ hr. So, 24/x + 24/(7 - x) = 14 x 2 - 98x + 168 = 0 (x - 3)(x - 4) = 0 => x = 3 or 4. Since, P is faster than Q, so P's speed = 4 km/hr and Q's speed = 3 km/hr.

Question 19

Karthik could cover a distance of 200 km in 22 days while resting for 2 hrs. per day. In how many days (approx) he will cover a distance of 250 km while resting for 2 hrs. per day and moving with 2/3rd of the previous speed ?

Accepted Answer

Given Karthik can cover the distance of 200 kms resting 2 hrs per day in 22 days. Let the initial speed be '1' Hence, Time = 22(24hrs - 2) Noe new speed = 2/3 Let the number of days he take be 'D' Therefore, 22 24 - 2 x 3 200 = D 24 - 2 x 2 250 D = 11 x 3 x 5/4 = 41.25 days. = 41 1/4 days.

Question 20

A 200 m long train passes a motorcycler, running in the same direction at 12 km/hr, in 15 second and a jeep travelling in the same direction in 20 s. At what speed is the car travelling (length of both the motorcycler and jeep is negligible)?

Accepted Answer

Let the speed of the train be 'S' kmph From the given data, Distance = Length of train = D = 200 mts = 200 x 18/5 kms Time = 10 sec given speed of the motorcycler = 12 kmph Relative speed as they are moving in the same direction = (S - 12) kmph ( S - 12) = 200 x 18 5 15 S - 12 = 48 S = 60 kmph Hence, the speed of the train = S = 60 kmph Now, Let the speed of the jeep be 'x' kmph 60 - x = 200 x 18 5 20 60 - x = 36 x = 60 - 36 x = 24 kmph Therefore, the speed of the jeep = x = 24 kmph.

Time and Distance Questions