- A man completes his journey in 8 hours. He covers half the distance at 40 kmph and the rest at 60 kmph. The length of the journey is?

A) 384 km

B) 420 km

C) 450 km

D) Cannot be determined

Answer:

Explanation: Since, he travelled equal distance at 40 kmph and 60 kmph, the ratio of time taken should be 60 : 40

Ie, 3 : 2

Hence he took 23+2=25th23+2=25thtime of the 8 hours, travelling half the distance at 60 kmph.

Hence he travelled at 60 kmph for 25×8=3.2 hours25×8=3.2 hours

Distance travelled at 60 kmph = 3.2 × 60

= 192 km

Total distance travelled = 192 × 2= 384 km

- A man performs 2/15 of the total journey by train. 2/20 by bus and the remaining 10 km on foot. His total journey in km is

A)15.6

B) 13.04

C) 16.4

D) 12.8

Answer:

Explanation: Let total journey be ‘x’ km.

A man performs 2/15 of the total journey by train. 2/20 by bus and the remaining 10 km on foot.

∴(2/15)*x*+(2/20)*x*+10=*x*⇒*x*

⇒ x = 13.04 km

- A farmer travelled a distance of 61 Km in 9hrs. He travelled partly on foot at the rate of 4km/hr and partly on bicycle at the rate of 9km/hr. The distance travelled in km on foot is :

A)17

B)16

C)14

D)15

Answer:B

Explanation: Time = distance/speed

Given,

Total distance = 61 Km

Let the distance travelled on foot = d km

∴ Distance travelled on bicycle = (61 – d) km

Given, speed on foot = 4km/hr

∴ Time taken to travel on foot = (d/4) hr

Speed on cycle = 9 km/hr

∴ Time taken to travel on cycle = (61-d)/9

Total time taken = (frac{d}{4} + frac{{61 – d}}{9})

Given, Total time = 9hrs

(therefore frac{d}{4} + frac{{61 – d}}{9} = 9)

⇒ 9d + 244 – 4d = 324

⇒ 5d = 80

⇒ d = 16 Km

- A,B and C start from the same place to walk around a circular path of length 12 km. A walks at the rate of 4 kmph, B at 8 kmph and C at 3/2 kmph. They will meet together at the starting place at the end of :

A) 10 hours

B) 12 hours

C) 15 hours

D) 24 hours

Answer:D

Explanation: Time taken by A, B, C to cover circular path is 12/4, 12/8, 12/(1.5) respectively

Time interval after which they will all meet at starting point = LCM of 3, 8, 1.5

= LCM (3, 8, 1.5)

= 24 hours

- Two cars travel from city A to city B at a speed of 42 and 60 km/hr respectively. If one car takes 2 hours lesser time than the other car for the journey, then the distance between City A and City B is:

A) 336 km

B) 280 km

C) 420 km

D) 224 km

Answer:B

Explanation: Let the distance between the city A and city B be ‘x’ km.

Speed of car 1 = 42 km/hr

Speed of car 2 = 60 km/hr

We know that,

Time = Distance/Speed

Time taken by car 1 to travel from city A to city B = x/42

Time taken by car 2 to travel from city A to city B = x/60

(x/42) – (x/60) = 2 (∵ one car takes 2 hours lesser time than the other car)

x = 280 km

∴ The distance between City A and City B = 280 km

- Pihu and Aayu are running on a circular track of diameter 28 m. Speed of Pihu is 48 m/s and that of Aayu is 40 m/s. They start from the same point at the same time in the same direction. When will they meet again for the first time?

A) 8 seconds

B) 11 seconds

C) 13 seconds

D) 14 seconds

Answer:B

Explanation: As per the given data,

Length of the circular track = π × d = π × 28 m

Given that Pihu and Aayu are running in the same direction at the same point

We know that when two persons A and B running around a circular track of length L mts with speed of a, b m/s in the same direction

They meet each other at any point on the track = L/(a – b) sec

= 28 π/(48 – 40)

= 11 sec

- A car driver leaves Bangalore at 8.30 A.M. and expects to reach a place 300 km from Bangalore at 12.30 P.M. At 10.30 he finds that he has covered only 40% of the distance. By how much he has to increase the speed of the car in order to keep up his schedule?

A) 45 km/hr

b) 40 km/hr

C) 35 km/hr

D) 30 km/hr

Answer:D

Explanation: Speed = distance/time

Let the original speed be ‘v’ km/hr

Given, car driver leaves Bangalore at 8.30 A.M. and expects to reach a place 300 km from Bangalore at 12.30 P.M.

Time of journey = 4 hours

Given, at 10:30 he found that he has covered 40% of the distance.

Distance covered = 40% of 300 = 120 km

Time to cover this 120 km = 2 hours

∴ Speed = 120/2 = 60 km/hr

Distance to be covered = (300 – 120) = 180 km

Time left = 4 – 2 = 2 hours

∴ Speed at which he has to travel = 180/2 = 90 km/hr

∴ Increase in speed = 90 – 60 = 30 km/hr

- In a 100 m race, A beats B by 15 mand C by 18 m. In a race of 170 m, B will beat C by

A) 6 m

B) 10 m

C) 8 m

D) 9 m

Answer:A

Explanation: Let, x, y and z are the distances covered by A,B and C respectively

Given, In a 100 m race, A beats B by 15 mand C by 18 m

∴ Ratio of distance covered by A and B,

x : y = 100: 85⇒ x/y = 100/85

Ratio of distance covered by A and C,

x: z = 100: 82⇒ x/z = 100/82

∴ y : z = 85: 82

∴ When B covers 85 m, distance covered by C = 82 m

∴ When B covers 170 m, distance covered by C = (82/85) × 170 = 164 m

∴ B will beat C by = 170 m – 164 m = 6 m

- A boat goes 15 km an hour in still water, and takes thrice the time to cover the same distance upstream. The speed of the current (in km / hr) is –

A) 10 km/hr

B) 12 km/hr

C) 13 km/hr

D) 14 km/hrs

Answer:A

Explanation: Let the speed of stream be ‘a’ and speed of boat be ‘b’.

In still water, speed of boat = b

In upstream speed of boat relative to stream = b – a

Given, boat goes 15 km an hour in still water, and takes thrice the time to cover the same distance upstream.

Speed = distance/time

b = 15/1

⇒ b = 15 km/hr

b – a = 15/3

⇒ b – a = 5

⇒ a = b – 5 = 10 km/hr

10.A man can row at 7 km/hour in still water. He finds that it takes twice the time to row upstream than the time to row downstream. The speed of the stream is

A) 2.6 km/hour

B) 7 km/hour

C) 2.3 km/hour

D) 4 km/hour

Answer:C

Explanation: The speed of the stream is y km/hour (say)

Hence upstream speed will be (7 – y) km/hour

And downstream speed will be (7 + y)km/hour

it takes twice the time to row upstream than the time to row downstream. Hence, speed of downstream is twice than the speed of upstream.

According to the problem, 7 + y = 2(7 – y)

⇒7 + y = 14 – 2y

⇒3y = 7

⇒y = 2.33

Speed of the stream = 2.33 km/hour

11.A boat goes 10kms an hour in still water, but takes twice as much time in going the same distance against the current. The speed of the current (in km/hr) is –

A) 2 km/hr

B) 4 km/hr

C) 3 km/hr

D) 5 km/hr

Answer:D

Explanation: Speed of Boat in Current = Speed of Boat in still water – Speed of Current

A boat goes 10 kms an hour in still water

∴ Speed of Boat in still water = 10km/hr

Let it travels for 1 hr and covered 10 km

It takes twice as much time in going the same distance against the current

Thus, it will take 2 hr to cover the same distance of 10 km

∴ Speed of Boat against Current = 10km / 2hrs = 5km/hr

Speed of Current = 10km/hr – 5km/hr = 5km/hr

12.A boat goes downstream in one-third the time it takes to go upstream. Then the ratio between the speed of boat in still water and speed of the stream is

A) 5 : 1

B) 3 : 2

C) 1 : 2

D) 2 : 1

Answer:D

Explanation: Let the speed of boat be ‘a’ and speed of stream be ‘b’.

Relative speed of boat going upstream = a – b

Relative speed of boat going downstream = a + b

Given, boat goes downstream in one-third the time it takes to go upstream.

Time = distance/speed

Distance is same in both cases.

(therefore frac{d}{{a + b}} = frac{1}{3} times frac{d}{{a – b}})

⇒ 3a – 3b = a + b

⇒ a = 2b

⇒ a : b = 2 : 1

13.The speed of a boat along the stream is 12 km/h and against the stream is 8 km/h. the time taken by the boat to sail 24 km in still water is

A) 2 h

B) 3 h

C) 2.4 h

D) 1.2 h

Answer:C

Explanation: Let the speed of the boat be C and the velocity of the stream be V.

Hence,

C + V = 12 and

C – V = 8

Adding both the equations to eliminate V, we have

2C = 20

⇒ C = 10 kmph

Hence, the time taken by the boat to cover 24 km in still water = 24/10 = 2.4 h

14.A boat running at a speed of 34 km/h downstream covers a distance of 4.8 km in 8 minutes. The same boat while running upstream at same speed covers the same distance in 9 minutes. What is the speed of the current?

A) 2.4 km/h

B) 3 km/h

C) 2 km/h

D) 3.2 km/h

Answer:C

Explanation: Let the speed of the water current be ‘x’ km/hr

__Downstream:__

While going downstream,

Total speed = speed of the boat + speed of the water current

⇒ Total speed = 34 + x

Distance covered = 4.8 km

Time taken = 8 min = 0.133 hrs

We know that

Speed = Distance/Time

⇒ 34 + x = 4.8/0.133

⇒ 34 + x = 36

⇒ x = 2

Thus speed of the Current is 2 km/hr

(The same can be confirmed using the upstream condition where the total speed will be the difference between the speed of the boast and that of the current)

15.A boat is rowed downstream at 15.5 km/hr and upstream 8.5 km/hr. The speed of the stream is

A) 3.5 km/hr

B) 5.75 km/hr

C) 6.5 km/hr

D) 7 km/hr

Answer:A

Explanation: Let the speed of boat in still water be x and that of stream be y, so we have the following equations,

x + y = 15.5 km/hr …(1)and,

x – y = 8.5 km/hr …(2)

Now we subtract (2) from (1) we get,

⇒ 2y = 7 km/hr

⇒ y = 3.5 km/hr

- A steamer running downstream covers a distance of 30 km in 2 hours. While coming back the steamer takes 6 hours to cover the same distance. If the speed of the current is half of that of the steamer, then find the speed of the steamer in kmph.

A) 10 kmph

B) 12 kmph

C) 18 kmph

D) 20 kmph

Answer:A

Explanation: Speed of the steamer downstream S_{d} = 30/2 = 15 kmph

Speed of the steamer upstream S_{u} = 30/6 = 5 kmph

Let speed of the steamer be ‘x’, then speed of the current would be (x/2).

According to the question,

x + (x/2) = 15 ……………..(1)

x – (x/2) = 5 ………………..(2)

From equations (1) and (2) we get,

2x = 20 ⇒ x = 10 kmph

Hence, speed of the steamer is 10 kmph.

17.In a fixed time, a boy swims double the distance along the current that he swims against the current. If the speed of the current is 3 kmph, the speed of the boy in still water is:

A) 6 kmph

B) 9 kmph

C) 10 kmph

D) 12 kmph

Answer:B

Explanation: We know that Speed = Distance/Time

Let speed of boy in still water be g kmph.

Then speed of boy in upstream = g – 3 kmph

Speed of boy in downstream = g + 3 kmph

We have the boy covering double the distance in downstream than in upstream in the same time.

Hence, the speed of boy in downstream should be double his speed in upstream

Hence,

We have

⇒ (g + 3) = 2 × (g – 3)

⇒ g + 3 = 2g –

⇒ g = 9 kmph

18.A bus covers a distance in 6 minutes. If it runs at 30 kmph on an average speed, then the speed at which the bus should run to increase the time of journey to 30 minutes will be –

A) 5 kmph

B) 8 kmph

C) 6 kmph

D) 7 kmph

Answer:C

Explanation: We know that, Distance traveled = Average speed × Time required

Given, Average velocity = 30 kmph

= (30/60) km/min ———– (1 Hour = 60 Minutes)

= 0.5 km/min

Time required = 6 min

∴ Distance traveled = (0.5 × 6) km = 3 km

Now, Time required = 30 min

∴ Average speed = Distance traveled/Time required

= 3 km/30 min

= 0.1 km/min

= 0.1 × 60 kmph ———– (1 Hour = 60 Minutes)

= 6 kmph

19.In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

A) 1 hour

B) 2 hours

C) 3 hours

D) 4 hours

Answer:A

Explanation: Let, the original duration of flight be t hrs.

∵ Average Speed = Total Distance / Time

Total Distance of the flight is 600 km.

So, original average speed = 600/t

Due to bad weather speed of trip is reduced by 200 km/hr and time of flight is increased by 30 minutes i.e. 0.5 hr.

∴ Reduced average speed = (600/t) – 200

And New duration of flight = (t + 0.5) hrs

So, the new average speed = 600/(t + 0.5)

Equating,

(begin{array}{l} Rightarrow frac{{600}}{t}-200 = frac{{600}}{{t + 0.5}}\ Rightarrow frac{3}{t}-1 = frac{3}{{t + 0.5}}\ Rightarrow frac{{3-t}}{t} = frac{3}{{t + 0.5}} end{array})

⇒ t^{2} + 0.5t – 1.5 = 0

⇒ 2t^{2} + t – 3 = 0

⇒ 2t^{2} – 2t + 3t – 3 = 0

⇒ (t – 1)(2t + 3) = 0

⇒ (t – 1) = 0

∴ t = 1 hr

20.How does a train 220 meters long, running at the rate of 54 km an hour, take to cross a bridge 120 meters in length?

A) 28.33 seconds

B) 22.67 seconds

C) 20.67 seconds

D) 19 seconds

Answer:C

Explanation: We know that speed = distance/time

Speed of train = 54 kmph

= 15 m/s

Total distance to be covered = Length of train + Length of the bridge

= 220 + 120

= 340 m

Time taken = 340/15

= 22.67 seconds