161. A boat covers a certain distance downstream in 8 hours but takes 12 hours to return upstream to the starting place. If the boat covers 200 km in still water in 5 hours, then find the speed of the stream?

एक नाव धारा के अनुकूल एक निश्चित दूरी 8 घंटे में तय करती है लेकिन धारा के प्रतिकूल अपने शुरुआती स्थान पर लौटने में 12 घंटे का समय लेती है। यदि नाव स्थिर जल में 200 किमी की दूरी 5 घंटे में तय करती है, तो धारा की गति ज्ञात कीजिए?

A. 8 km/hr
B. 12 km/hr
C. 6 km/hr
D. 10 km/hr
E. None of these

Option “A” is correct.

The ratio of the downstream to the upstream speed of the boat = 12:8 = 3:2

Let the downstream speed of the boat = 3x

And the upstream speed of the boat = 2x

The speed of the boat in still water = 200/5 = 40 km/hr

(3x + 2x)/2 = 40

5x = 80

x = 16

The speed of the stream = (3 * 16 – 2 * 16)/2 = (48 – 32)/2 = 16/2 = 8 km/hr

162. A boat covers 30 km downstream and return to the starting point in 8 hours. If the speed of the boat in still water is twice the speed of the stream, then find the speed of the boat in still water.

एक नाव धारा के अनुकूल 30 किमी की दूरी तय करती है और 8 घंटे में प्रारंभिक बिंदु पर लौट आती है। यदि स्थिर जल में नाव की गति धारा की गति से दोगुनी है, तो स्थिर जल में नाव की गति ज्ञात कीजिए।

A. 8 km/hr
B. 12 km/hr
C. 10 km/hr
D. 6 km/hr
E. None of these

Option “C” is correct.

Let the speed of the stream = 1a

And the speed of the boat in still water = 2a

According to question,

30/(2a + 1a) + 30/(2a – 1a) = 8

30/3a + 30/1a = 8

10 + 30 = 8a

a = 40/8

a = 5

Therefore, speed of the boat in still water = 2 * 5 = 10 km/hr

163. A boat goes 35 km downstream and while returning covered only 80% of the distance that is covered in downstream. If the boat takes 6 hours more to cover upstream than downstream, then find the approximate speed of boat in still water if the speed of the stream is (10/9)m/s?

एक नाव धारा के अनुकूल 35 किमी जाती है और लौटते समय धारा के अनुकूल तय की गई दूरी का केवल 80% ही तय करती है। यदि नाव धारा के प्रतिकूल दूरी तय करने में धारा के प्रतिकूल से 6 घंटे अधिक लेती है, तो स्थिर जल में नाव की अनुमानित गति ज्ञात कीजिए यदि धारा की गति (10/9) मीटर/सेकंड है?

A. 9 km/hr
B. 13 km/hr
C. 5 km/hr
D. 11 km/hr
E. None of these

Option “E” is correct.

Speed of current = (10/9) × (18/5) => 4 km/hr

Let the speed of boat in still water = x km/hr

Then, according to the question,

[(35 × 80/100)/(x – 4)] – [(35)/(x + 4)] = 6

(28x + 112 – 35x + 140)/(x – 4) (x + 4) = 6

-7x + 252 = 6x² – 96

6x² + 7x – 348 = 0

Solving we get = x ≈ 7 km/hr

Hence, the required answer = 7 km/hr.

164. Sum of the downstream and upstream speed of the boat is 56 km/hr and the distance covered by the boat in downstream in 15 hours is 120 km less than the distance covered by the boat in upstream in 25 hours. Find the speed of the current?

नाव की धारा के अनुकूल और धारा के प्रतिकूल गति का योग 56 किमी/घंटा है और नाव द्वारा धारा के अनुकूल 15 घंटे में तय की गई दूरी, धारा के प्रतिकूल नाव द्वारा 25 घंटे में तय की गई दूरी से 120 किमी कम है। धारा की गति ज्ञात कीजिये?

A. 5 km/hr
B. 3 km/hr
C. 2 km/hr
D. 4 km/hr
E. None of these

Option “D” is correct.

Let the speed of the boat in still water be B km/hr and the speed of the current be C km/hr

B + C + B – C = 56

2B = 56

B = 28 km/hr

(28 – C) * 25 – (28 + C) * 15 = 120

700 – 25C – 420 – 15C = 120

280 – 120 = 40C

160 = 40C

C = 4 km/hr

165. Downstream speed of the boat is 9/7th of the speed of the boat in still water and the time taken by the boat to cover 240 km in upstream is 12 hours. Find the speed of the stream.

नाव की धारा के अनुकूल गति, स्थिर जल में नाव की गति का 9/7 है और नाव द्वारा धारा के प्रतिकूल 240 किमी की दूरी तय करने में 12 घंटे का समय लगता है। धारा की गति ज्ञात कीजिए।

A. 8 km/hr
B. 5 km/hr
C. 6 km/hr
D. 4 km/hr
E. None of these

Option “A” is correct.

Downstream speed of the boat = 9x km/hr

Speed of the boat in still water = 7x km/hr

Speed of the stream = 9x – 7x = 2x km/hr

Upstream speed of the boat = 7x – 2x = 5x km/hr

5x = 240/12

5x = 20

x = 4 km/hr

Speed of the stream = 2 * 4 = 8 km/hr

166. A boat takes equal time to travel a distance of 81 km in upstream and 99 km in downstream. If the speed of the boat in still water is 20km/hr, then what is the speed of the current (in km/hr)?

एक नाव धारा के प्रतिकूल 81 किमी और धारा के अनुकूल 99 किमी की दूरी तय करने में बराबर समय लेती है। यदि स्थिर जल में नाव की गति 20 किमी/घंटा है, तो धारा की गति (किमी/घंटा में) क्या है?

A. 3 km/hr
B. 4 km/hr
C. 2 km/hr
D. 2.5 km/hr
E. None of these

Option “C” is correct.

Let the speed of the current be x km/h

According to question,

81/(20 – x) = 99/(20 + x)

9/(20 – x) = 11/(20 + x)

180 + 9x = 220 – 11x

20x = 40

x = 2

Hence, the speed of current = 2 km/h

167. The upstream speed and downstream speed of the boat is 28 kmph and 36 kmph respectively. Find the time taken to cover the distance 224km in still water.

नाव की उर्ध्वप्रवाह गति और अनुप्रवाह गति क्रमशः 28 किमी प्रति घंटा और 36 किमी प्रति घंटा है। शांत जल में 224 किमी की दूरी तय करने में लगने वाला समय ज्ञात कीजिए।

A. 6 hours
B. 7 hours
C. 8 hours
D. 6.2 hours
E. None of these

Option “B” is correct.

Speed of the boat in still water = (28 + 36)/2 = 32 kmph

Required time = 224/32 = 7 hours

168. A boat travel 120 km against stream in 20 hours and the speed of the stream is 12 kmph. What is the speed of the boat along with stream?

एक नाव 20 घंटे में 120 किमी ऊर्ध्वप्रवाह की यात्रा करती है और धारा की गति 12 किमी प्रति घंटा है। धारा के साथ नाव की गति क्या है?

A. 30 kmph
B. 28 kmph
C. 24 kmph
D. 20 kmph
E. None of these

Option “A” is correct.

Upstream speed = 120/20 = 6 kmph

Stream speed = 12 kmph

Boat in still water = 12 + 6 =18 kmph

Speed of the boat along with stream = 18 + 12 = 30 kmph

169. Ravi can row downstream at 18 Km/hr and upstream at 14 Km/hr. Find the speed of Ravi in still water and speed of current.

रवि 18 किलोमीटर/घंटा अनुप्रवाह नाव चला सकता है और 14 किमी/घंटा ऊर्ध्वप्रवाह नाव चला सकता है। स्थिर पानी में रवि की गति और धारा की गति ज्ञात करें।

A. 16Km/h and 2Km/h
B. 15Km/h and 3Km/h
C. 14Km/h and 4Km/h
D. 13Km/h and 2Km/h
E. 15Km/h and 5Km/h

Option “A” is correct.

Downstream speed = 18Km/h

Upstream speed = 14 Km/h

Speed in still water = ½ * (18 + 14)

= 16 Km/h

Speed of current = 1/2(18-14) = 2 Km/h

170. If the time taken by a boat to travels 30 km upstream is twice the time taken by that boat to travel 75 km downstream. If the speed of the stream is 10 kmph, what is the speed of the boat in still water?

यदि एक नाव द्वारा 30 किमी ऊर्ध्वप्रवाह दूरी तय करने में लगने वाला समय 75 किमी अनुप्रवाह यात्रा करने में लगा समय से दोगुना है। यदि धारा की गति 10 किमी प्रति घंटा है, तब स्थिर पानी में नाव की गति क्या है?

A. 20 kmph
B. 15 kmph
C. 25 kmph
D. 30 kmph
E. None of these

Option “B” is correct.

Speed of the boat in still water=x

30/(x – 10) = 2 * [75/(x + 10)]

30(x + 10) = 150 * (x – 10)

30x + 300 = 150x – 1500

120x = 1800

x = 15 kmph

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