1. A train without stoppage travels with an average speed of 50 km/h, and with stoppage, it travels with an average speed of 40 km/h. For how many minutes does the train stop on an average per hour?

स्टॉपेज के बिना एक ट्रेन 50 किमी/घंटा की औसत गति से यात्रा करती है, और स्टॉपेज के साथ, यह 40 किमी/घंटा की औसत गति से यात्रा करती है। ट्रेन प्रति घंटे औसतन कितने मिनट रुकती है?

Option “C” is correct.

Without stoppage average speed = 50 km/h

With stoppages average speed = 40 km/h

As we know,

Time of rest per hour equal to the difference in average speed divided by the speed without stoppage.

Required time = [(50 – 40)/50] × 60 = 12

So, A train stops on an average 12 minute/hr

2. A train without stoppage travels with an average speed of 72 km/h and with stoppage, it travels with an average speed of 60 km/h. For how many minutes does the train stop on an average per hour?

A रेलगाड़ी बिना किसी अवरोध के 72 किमी/घंटे की औसत गति से चलती है और अवरोध के साथ, यह 60 किमी/घंटे की औसत गति से चलती है। रेलगाड़ी प्रति घंटे औसतन कितने मिनट रुकती है?

Option “C” is correct.

Without stoppage average speed = 72 km/h

With stoppages average speed = 60 km/h

As we know,

Time of rest per hour equal to the difference in average speed divided by the speed without stoppage.

Required time = [(72 – 60)/72] × 60 = 10

So, A train stops on an average 10 minute/hr

3. A train covers 108 km in 3 hours with a constant speed of V1 and certain distance with a constant speed of Vin next 2 hours. If the average speed of the train is 43.2 km/hour, then find the difference between V2 and V1?

एक ट्रेन V1 की स्थिर गति के साथ 3 घंटे में 108 किमी और अगले 2 घंटों में V2 की स्थिर गति के साथ कुछ दूरी तय करती है। यदि ट्रेन की औसत गति 43.2 किमी/घंटा है, तो V2 और V1 में अंतर ज्ञात कीजिये।

Option “A” is correct.

Distance covered by the train with speed V= 108 km

Distance covered by the train with speed V2 = V× 2 = 2 V2

So, total distance covered = 108 + 2 V2

Total time = 3 + 2 = 5 hours

Now we can use,

Average speed = total distance /total time

⇒ 43.2 = (108 + 2 V2)/5

⇒ (108 + 2 V2) = 43.2 × 5

⇒ (108 + 2 V2) = 216

⇒ 2 V2 = 108

⇒ V= 54

Now,

V1 = 108/3 = 36 km/hour

So, the required difference = V2 – V= 54 – 36 = 18

∴ The difference between V2 and V1 is 18.

4. The average speed of a car is 600 metres/minute. How much slower (in metres/second) does the car run than a sprinter who covers 100 metres in 9.6 seconds?

एक कार की औसत गति 600 मीटर/मिनट है। 9.6 सेकंड में 100 मीटर की दूरी तय करने वाले स्प्रिंटर की तुलना में इस कार की गति कितनी धीमी (मीटर/सेकंड में) है?

Option “D” is correct.

The average speed of a car = 600 metres/minute = 10 m/s

⇒ Speed = distance/time

⇒ The average speed of a sprinter = 100/9.6 m/s

⇒ Difference of the average speed of car and sprinter = (100/9.6) – 10

⇒ Difference of the average speed of car and sprinter = 40/96 = 5/12 m/s

∴ The car runs (5/12) m/s slower than a sprinter.

5. The distance between two stations, A and B, is 428 km. a train starts from station ‘A’ at 6:00 a.m and moves towards station ‘B’ at an average speed of 48 km/h. Another train starts from station ‘B’ at 6:20 a.m and moves towards statin ‘A’ at an average speed of 55 km/h. At what time will the trains meet?

दो स्टेशनों, A और B के बीच की दूरी, 428 किमी है। एक ट्रेन स्टेशन ’A’ से सुबह 6:00 बजे शुरू होती है और 48 किमी/घंटा की औसत गति से स्टेशन ‘B’ की ओर बढ़ती है। एक अन्य ट्रेन सुबह 6:20 बजे स्टेशन ‘B’ से शुरू होती है और 55 किमी/घंटा की औसत गति से स्टेशन ‘A’ की ओर बढ़ती है। ट्रेनें किस समय पर एक दुसरे से मिलेंगी ?

Option “C” is correct.

Distance between A and B = 428 km

Speed of first train = 48 km/hr

Distanced covered in 20 min by first train = 48/60 × 20 = 16 km

Remaining distance = 428 – 16 = 412 km

Speed of second train = 55 km/hr

If both train running opposite train, then relative speed = 48 + 55 = 103 km/hr

Time = distance/speed = 412/103 = 4 hr

∴ Train meet each other = 6 : 00 + 0 : 20 + 4 : 00 = 10 : 20 a. m

6. A bus travels 150 Km in 3 hours and then travel next 2 hours at 60 Km/hr. Then the average speed of the bus will be

एक बस 3 घंटे में 150 किलोमीटर की यात्रा करती है और फिर अगले 2 घंटे 60 किमी/घंटे पर यात्रा करती है। तब बस की औसत गति होगी

Option “B” is correct.

Distance covered in 2 hrs with the speed of 60 km/hr = 2 × 60 = 120

Total distance = 150 + 120 = 270

Total time = 2 + 3 = 5 hrs

As we know,

Average speed = Total distance/Total Time

∴ Average speed = 270/5 = 54 km/hr

7.A man goes to a place on the car at a speed of 160 km/h and comes back at a lower speed. If the average speed is 64km/h in total, then return speed (in km/h) is:

एक आदमी किसी स्थान पर कार द्वारा 160 किमी/घंटे की गति से जाता है और कम गति से वापस आता है। यदि कुल मिलाकर औसत गति 64 किमी/घंटा है, तो वापसी गति (किमी/घंटा में) क्या है?

Option “B” is correct.

Let return speed of man be x, Average speed = 64 km/hr

As we know,

Average speed = 2xy/(x + y)

⇒ 64 = (2 × 160 × x)/(160 + x)

⇒ 160 + x = 320x/64

⇒ 160 + x = 5x

⇒ 4x = 160

⇒ x = 160/4

⇒ x = 40 km/hr

8. Travelling at 66 km/h, Piyali reaches a place 5 minutes early. If she travelled at 54 km/h, she would have been 3 minutes late. What is the distance Piyali had to travel?

66 किमी/घंटे की गति से यात्रा करते हुए पियाली 5 मिनट पहले पहुंचती है। यदि वह 54 किमी/घंटे की गति से यात्रा करती, तो उसे 3 मिनट की देरी होती। पियाली को कितनी दूरी तय करनी थी?

Option “C” is correct.

Let the total distance be x km

We know time = distance/speed,

Time taken to travel at 66 km/hour = x/66 hour and,

Time taken to travel at 54 km/hour = x/54 hour.

Total difference in time = 5 minutes + 3 minutes = 8 minutes or 8/60 hours.

⇒ x/54 – x/66 = 8/60 hours

∴ x = 39.6 km.

∴ Total distance travelled = 39.6 km.

9. Puneet goes to his office at the speed of 60 km/hour and returns to his home at the speed of 90 km/hr. What will be the average speed of Puneet for the whole journey?

पुनीत 60 किमी / घंटे की गति से अपने कार्यालय जाता है और 90 किमी / घंटा की गति से अपने घर लौटता है। पूरी यात्रा के लिए पुनीत की औसत गति क्या होगी?

Option “C” is correct.

Average speed = 2 × 60 × 90/(60 + 90) = 2 × 5400/150

∴ Average speed = 72 km/hour

10. The ratio between the speed of Pillu, Chillu, and Tillu is 5 ∶ 7 ∶ 4 respectively. The mean value of the speed of Pillu, Chillu, and Tillu is 48 km/hr together. What is the mean value of the speed of Pillu and Chillu?

पिल्लू, चिल्लू और टिल्लू की चाल का अनुपात क्रमशः 5 : 7 : 4 है। यदि पिल्लू, चिल्लू और टिल्लू की माध्य मान 48 किमी/घंटा है, तो पिल्लू और चिल्लू की चाल का माध्य मान क्या हैं?

Option “C” is correct.

The ratio between the speeds of Pillu, Chillu, and Tillu = 5 ∶ 7 ∶4

Then,

Let the speed of Pillu, Chillu, and Tillu be 5x Km/hr, 7x Km/hr, and 4x Km/hr respectively.

Then total speed of Pillu, Chillu, and Tillu

⇒ 5x + 7x + 4x = 16x km/hr      —-(i)

The average speed of Pillu, Chillu, and Tillu = 48 km/hr

So the total speed of Pillu, Chillu, and Tillu = 48 × 3 = 144 km/hr

Now by equation (i) and (ii), we get

⇒ 16x = 144

⇒ x = 9 km/hr

Now the speed of Pillu = 5x = 5 × 9 = 45 km/hr

And the speed of Chillu = 7x = 7 × 9 = 63 km/hr

Now to find the mean speed of Pillu and Chillu

⇒ (The speed of Pillu + the speed of Chillu)/2

⇒ (45 + 63)/2 = 108/2 = 54 km/hr

∴ The average speed of Pillu and Chillu is 54 km/hr

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