191. A boat covers 54 km downstream in 90 minutes and the same boat covers 70 km upstream in 150 minutes. Find the time taken by the boat covers 160 km in still water?

एक नाव धारा के अनुकूल 54 किमी की दूरी 90 मिनट में तय करती है और वही नाव धारा के प्रतिकूल 70 किमी की दूरी 150 मिनट में तय करती है। नाव द्वारा स्थिर जल में 160 किमी की दूरी तय करने में लिया गया समय ज्ञात कीजिए?

A. 4 hours
B. 10 hours
C. 8 hours
D. 5 hours
E. None of these

Option “D” is correct.

The downstream speed of the boat = 54/(90/60) = 54 * 60/90 = 36 km/hr

The upstream speed of the boat = 70/(150/60) = 70 * 60/150 = 28 km/hr

The speed of the boat in still water = (36 + 28)/2 = 64/2 = 32 km/hr

Required time = 160/32 = 5 hours

192. A boat covers 315 km downstream in 7 hours and the boat covers 135 km upstream in 9 hours. Find the difference between the time taken by the boat to cover 150 km upstream and the time taken by the boat to cover 120 km in still water.

एक नाव 7 घंटे में धारा के अनुकूल 315 किमी की दूरी तय करती है और नाव धारा के प्रतिकूल 135 किमी की दूरी 9 घंटे में तय करती है। नाव द्वारा धारा के प्रतिकूल 150 किमी की दूरी तय करने में लगे समय और नाव द्वारा स्थिर जल में 120 किमी की दूरी तय करने में लिए गए समय के बीच का अंतर ज्ञात कीजिए।

A. 3 hours
B. 4 hours
C. 6 hours
D. 2 hours
E. None of these

Option “C” is correct.

The downstream speed of the boat = 315/7 = 45 km/hr

The upstream speed of the boat = 135/9 = 15 km/hr

The speed of the boat in still water = (45 + 15)/2 = 60/2 = 30 km/hr

Required difference = 150/15 – 120/30 = 10 – 4 = 6 hours

193. The speed of the boat in still water is five times the speed of the stream and the boat covers 240 km downstream and returns to the starting point in 10 hours, then in how many hours the boat covers 150 km in still water?

स्थिर जल में नाव की गति धारा की गति का पांच गुना है और नाव धारा के अनुकूल 240 किमी की दूरी तय करती है और 10 घंटे में प्रारंभिक बिंदु पर लौट आती है, तो कितने घंटे में नाव स्थिर जल में 150 किमी की दूरी तय करेगी?

A. 3 hours
B. 5 hours
C. 6 hours
D. 2 hours
E. None of these

Option “A” is correct.

Let the speed of the stream = x

And the speed of the boat in still water = 5x

240/(5x+1x) + 240/(5x-1x) = 10

240/6x + 240/4x = 10

40 + 60 = 10x

x = 100/10

x = 10

The speed of the boat in still water = 5*10 = 50 km/hr

Required time = 150/50 = 3 hours

194. The speed of the boat in still water is three times more than the speed of the stream and the boat covers 288 km upstream in 8 hours, then find the time taken by the boat to cover 144 km in still water?

स्थिर जल में नाव की गति धारा की गति से तीन गुना अधिक है और नाव 8 घंटे में धारा के प्रतिकूल 288 किमी की दूरी तय करती है, तो नाव को स्थिर जल में 144 किमी की दूरी तय करने में कितना समय लगेगा?

A. 2 hours
B. 6 hours
C. 4 hours
D. 3 hours
E. None of these

Option “D” is correct.

Let the speed of the stream = x km/hr

And the speed of the boat in still water = 4x km/hr

The downstream speed of the boat = 288/8 = 36 km/hr

4x – x = 36

3x = 36

x = 12

The speed of the boat in still water = 4 * 12 = 48 km/hr

Required time = 144/48 = 3 hours

195. Sum of the downstream and upstream speed of the boat is 50 km/hr and the difference between the downstream and upstream speed of the boat is 10 km/hr. Find the time taken by the boat to cover 240 km upstream?

नाव की धारा के अनुकूल और धारा के प्रतिकूल गति का योग 50 किमी/घंटा है और नाव की धारा के अनुकूल और धारा के प्रतिकूल गति के बीच का अंतर 10 किमी/घंटा है। नाव द्वारा धारा के प्रतिकूल 240 किमी की दूरी तय करने में लिया गया समय ज्ञात कीजिए?

A. 15 hours
B. 12 hours
C. 10 hours
D. 8 hours
E. None of these

Option “B” 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 = 50

2B = 50

B = 25 km/hr

B + C – B + C = 10

2C = 10

C = 5 km/hr

Required time taken = 240/(25 – 5) = 240/20 = 12 hours

196.  Speed of boat in still water is (x+2.5) km/hr. Boat covers 36 km in 2 hours in downstream. If the speed of the stream is 3 km/hr, find the time taken by boat to cover (x+15.5) km upstream?

स्थिर जल में नाव की गति (x+2.5) किमी/घंटा है। नाव धारा के अनुकूल 2 घंटे में 36 किमी की दूरी तय करती है। यदि धारा की गति 3 किमी/घंटा है, तो नाव द्वारा धारा के प्रतिकूल (x+15.5) किमी की दूरी तय करने में लिया गया समय ज्ञात कीजिए?

A. 2.33 hours
B. 3.33 hours
C. 5.33 hours
D. 3.78 hours
E. None of these

Option “A” is correct.

Downstream speed = x+2.5+3=36/2=18

x= 18-5.5=12.5

Required time = [12.5+15.5]/ (15–3)]=2.33 hours

197. A boat covers 216 km in still water in 6 hours and the ratio of the downstream speed of the boat to the upstream speed of the boat is 11:7. Find the sum of the time taken by the boat to cover 132 km downstream and 196 km upstream together?

एक नाव स्थिर जल में 216 किमी 6 घंटे में तय करती है और नाव की धारा के अनुकूल गति से नाव की धारा के प्रतिकूल गति का अनुपात 11:7 है। नाव द्वारा एकसाथ धारा के अनुकूल 132 किमी और धारा के प्रतिकूल 196 किमी की दूरी तय करने में लगने वाले समय का योग ज्ञात कीजिए?

A. 15 hours
B. 8 hours
C. 16 hours
D. 10 hours
E. None of these

Option “D” is correct.

Let the downstream speed of the boat = 11x

And the upstream speed of the boat = 7x

The speed of the boat in still water = 216/6 = 36 km/hr

(11x + 7x)/2 = 36

18x = 36 * 2

x = 4 km/hr

The downstream speed of the boat = 11 * 4 = 44 km/hr

The upstream speed of the boat = 7 * 4 = 28 km/hr

The time taken by the boat to cover 132 km downstream = 132/44 = 3 hours

The time taken by the boat to cover 196 km upstream = 196/28 = 7 hours

Required sum = 7 + 3 = 10 hours

198. A boat covers 60 km against the stream and 200 km along with stream in 25 hours. If the speed of the stream is 2/3rd of the speed of the boat in still water, then find the time taken by the boat to cover 48 km in still water?

एक नाव धारा के विपरीत 60 किमी और धारा के साथ 200 किमी की दूरी 25 घंटे में तय करती है। यदि धारा की गति स्थिर जल में नाव की गति की 2/3 है, तो नाव को स्थिर जल में 48 किमी की दूरी तय करने में कितना समय लगेगा?

A. 2 hours
B. 6 hours
C. 3 hours
D. 4 hours
E. None of these

Option “D” is correct.

Let the speed of the boat in still water = 3x

And the speed of the stream = 2x

200/(3x + 2x) + 60/(3x – 2x) = 25

200/5x + 60/1x = 25

40 + 60 = 25 * x

x = 100/25

x = 4

The speed of the boat in still water = 3 * 4 = 12 km/hr

Required time = 48/12 = 4 hours

199. A boat can travel 90 km upstream and 120 km downstream in 12 hours 30 minutes. What is the speed of the stream, if the boat can travel 60 km downstream in 2 hours 30 minutes?

एक नाव 90 किमी ऊर्ध्वप्रवाह और 120 किमी अनुप्रवाह दूरी 12 घंटे 30 मिनट में तय कर सकती है। यदि नाव 2 घंटे 30 मिनट में 60 किमी अनुप्रवाह यात्रा कर सकती है तो धारा की गति क्या है?

A. 5 kmph
B. 6 kmph
C. 8 kmph
D. 10 kmph
E. None of these

Option “B” is correct.

Distance = speed * time

Downstream speed = 60/2.5 = 24 kmph

120/24 + 90/x = 12.5

90/x = 12.5 – 5

x = 12 kmph

Speed of the upstream = 12 kmph

Speed of the stream = ½ * (24 – 12)

= 6 kmph

200. A fisherman goes 28 km along the stream and returning back to the same point in x hours. What is the value of x, if the speed of boat in still water is 12 km/hr and speed of stream is 2 km/hr?

एक मछुआरा धारा के साथ 28 किमी जाता है और x घंटे में उसी बिंदु पर वापस लौटता है। यदि ठहरे हुए पानी में नाव की गति 12 किमी / घंटा है और धारा की गति 2 किमी / घंटा है तो x का मान क्या है?

A. 3.2
B. 3.8
C. 4.2
D. 4.8
E. 5.2

Option “D” is correct.

Downstream speed of boat in River = 12 + 2 = 14 km/hr

Upstream speed of boat in River = 12 – 2 = 10 km/hr

So required time for the fisherman to return = 28/14 + 28/10

= 2 + 2.8

= 4.8 hours

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