151. The speed of the boat in still water is four times the speed of the stream and the boat covers 150 km along with the stream and 120 km against the stream in 7 hours, then find the speed of the boat in still water?

स्थिर जल में नाव की गति धारा की गति का चार गुना है और नाव धारा के साथ 150 किमी और धारा के विपरीत 120 किमी 7 घंटे में तय करती है, तो स्थिर जल में नाव की गति ज्ञात कीजिए?

A. 50 km/hr
B. 20 km/hr
C. 30 km/hr
D. 40 km/hr
E. None of these

Option “D” is correct.

Let the speed of the stream = x

And the speed of the boat in still water = 4x

150/(4x+1x) + 120/(4x-1x) = 7

150/5x + 120/3x = 7

30/x + 40/x = 7

70 = 7x

x = 10

The speed of the boat in still water = 4*10 = 40 km/hr
152. A boat covers 120 km downstream and 50 km upstream in 9 hours and the same boat covers 30 km upstream and 150 km downstream in 8 hours. Find the speed of the boat in still water?

एक नाव 9 घंटे में 120 किमी धारा के अनुकूल और 50 किमी धारा के प्रतिकूल की दूरी तय करती है और वही नाव 8 घंटे में 30 किमी धारा के प्रतिकूल और 150 किमी धारा के अनुकूल की दूरी तय करती है। स्थिर जल में नाव की गति ज्ञात कीजिए?

A. 20 km/hr
B. 45 km/hr
C. 30 km/hr
D. 15 km/hr
E. None of these

Option “A” is correct.

Let the downstream speed of the boat = x km/hr

And the upstream speed of the boat = y km/hr

120/x + 50/y = 9 —(1)

150/x + 30/y = 8 —(2)

From (1) and (2),

360/x + 150/y = 27

– 750/x – 150y = – 40

390/x = 13

x = 30

Sub x=30 in equation (1)

120/30 + 50/y = 9

50/y = 9 – 4

y = 50/5

y = 10

The speed of the boat in still water = (30 + 10)/2 = 40/2 = 20 km/hr
153. The ratio of the speed of the boat upstream to the speed of the stream is 4:1. If the boat can travel a distance of 216 km downstream in 18 hours, then find the speed of the boat.

धारा के प्रतिकूल नाव की गति से धारा की गति का अनुपात 4:1 है। यदि नाव धारा के अनुकूल 216 किमी की दूरी 18 घंटे में तय कर सकती है, तो नाव की गति ज्ञात कीजिए।

A. 10 km/hr
B. 8 km/hr
C. 12 km/hr
D. 20 km/hr
E. None of these

Option “A” is correct.

Let the speed of the boat upstream and the speed of the stream are 4x and x respectively.

Then Downstream speed of the boat = 4x + x + x = 6x

The downstream speed = 216/18 = 12 km/hr

6x = 12

x = 2 km/hr

Required answer = 6x – x = 5x = 5 * 2 = 10 km/hr
154. The time taken by a man to row 120 km along with the stream is one-third of the time taken by the man to row against the stream. Find the speed of the boat in still water, if the speed of stream is 10 km/hr?

एक व्यक्ति द्वारा धारा के साथ 120 किमी की दूरी तय करने में लिया गया समय, व्यक्ति द्वारा धारा के विपरीत लिए गए समय का एक तिहाई है। स्थिर जल में नाव की गति ज्ञात कीजिए, यदि धारा की गति 10 किमी/घंटा है?

A. 24 km/hr
B. 20 km/hr
C. 18 km/hr
D. 14 km/hr
E. None of these

Option “B” is correct.

Let us take the speed of the boat in still water be x km/hr,

120/(x + 10) = (1/3)*(120/(x – 10))

x + 10 = 3x – 30

2x = 40

x = 20

Speed of the boat in still water = 20 km/hr
155. Distance travelled by boat in upstream is 125% of the distance travelled by the boat in downstream and the time taken by the boat to cover this downstream and upstream distance is 4 hours and 7.5 hours respectively. If the speed of the current is 5 km/hr, then find the speed of the boat in still water.

धारा के प्रतिकूल नाव द्वारा तय की गई दूरी धारा के अनुकूल नाव द्वारा तय की गई दूरी का 125% है और नाव द्वारा इस धारा के अनुकूल और धारा के प्रतिकूल दूरी को तय करने में लिया गया समय क्रमशः 4 घंटे और 7.5 घंटे है। यदि धारा की गति 5 किमी/घंटा है, तो स्थिर जल में नाव की गति ज्ञात कीजिए।

A. 30 km/hr
B. 25 km/hr
C. 20 km/hr
D. 18 km/hr
E. None of these

Option “B” is correct.

Let the speed of the boat in still water be B km/hr.

((B + 5) * 4)/((B – 5) * 7.5) = 4/5

(B + 5)/((B – 5) * 1.5) = 1/1

B + 5 = 1.5B – 7.5

0.5B = 12.5

B = 25 km/hr
156. A boat can cover 152 km downstream and 102 km upstream in 9 hours. If the ratio of the speed of the boat in still water to the speed of the stream is 7:1, then find the speed of the boat in still water.

एक नाव धारा के अनुकूल 152 किमी और धारा के प्रतिकूल 102 किमी 9 घंटे में तय कर सकती है। यदि स्थिर जल में नाव की गति से धारा की गति का अनुपात 7:1 है, तो स्थिर जल में नाव की गति ज्ञात कीजिए।

A. 28 km/h
B. 35 km/h
C. 14 km/h
D. 21 km/h
E. None of these

Option “A” is correct.

Let the speed of the boat in still water and speed of the stream be 7x km/h and x km/h respectively.

Speed of boat in upstream = 7x-x = 6x km/h

Speed of boat in downstream = 7x + x = 8x km/h

(102/6x) + (152/8x) = 9

= {(17+19)/x} = 9

36/x = 9

x = 4

So, speed of the boat in still water = 7 x 4 = 28 km/h
157. The time taken by the boat to cover 140 km downstream is 1/2 of the time taken by the boat to cover 120 km upstream. If the speed of the stream is 8 km/hr, then find the speed of the boat in still water.

नाव द्वारा धारा के अनुकूल 140 किमी की दूरी तय करने में लिया गया समय, नाव द्वारा 120 किमी धारा के प्रतिकूल तय करने में लगने वाले समय का 1/2 है। यदि धारा की गति 8 किमी/घंटा है, तो स्थिर जल में नाव की गति ज्ञात कीजिए।

A. 16 km/hr
B. 24 km/hr
C. 32 km/hr
D. 20 km/hr
E. None of these

Option “D” is correct.

Let the speed of the boat in still water = x

140/(x + 8)/(120/(x – 8)) = 1/2

140/(x + 8) = 120/(x – 8) * 1/2

140 * (x – 8) = 60 * (x + 8)

140x – 1120 = 60x + 480

80x = 1600

x = 20

The speed of the boat in still water = 20 km/hr
158. A boat covers a certain distance in downstream in 10 hours and a certain distance in upstream in 20 hours and the total distance travelled in downstream and upstream is 620 km. If the speed of the stream is 4 km/hr, then find the downstream speed of the boat.

एक नाव धारा के अनुकूल एक निश्चित दूरी 10 घंटे में और धारा के प्रतिकूल एक निश्चित दूरी 20 घंटे में तय करती है और धारा के अनुकूल और धारा के प्रतिकूल तय की गई कुल दूरी 620 किमी है। यदि धारा की गति 4 किमी/घंटा है, तो नाव की धारा के अनुकूल गति ज्ञात कीजिए।

A. 18 km/hr
B. 28 km/hr
C. 15 km/hr
D. 26 km/hr
E. None of these

Option “D” is correct.

Speed of the boat in still water = x

Speed of the current = 4 km/hr

(x + 4) * 10 + (x – 4) * 20 = 620

30x = 660

x = 22 km/hr

Downstream speed of the boat = 22 + 4 = 26 km/hr
159. The boat will take 2 hours to cover the distance of 20km in downstream and while covering the same distance in upstream it will take 5 hours. Find the speed of the current.

नाव को धारा के अनुकूल 20 किमी दूरी तय करने में 2 घंटे का समय लगेगा और धारा के प्रतिकूल उसी दूरी को तय करने में 5 घंटे का समय लगेगा। धारा की गति ज्ञात कीजिए।

A. 2kmph
B. 3kmph
C. 4kmph
D. 5kmph
E. None of these

Option “B” is correct.

Downstream speed=20/2=10kmph

Upstream speed=20/5=4kmph

Speed of the current=1/2*(10-4)=3kmph
160. The speed of the current is 4 km/hr. A boat goes 10 km upstream and comes back to starting point in 80 minutes. What is the speed of the boat in still water? (In km/hr)

धारा की गति 4 किमी/घंटा है। एक नाव धारा के प्रतिकूल 10 किमी जाती है और 80 मिनट में प्रारंभिक बिंदु पर वापस आती है। शांत जल में नाव की गति क्या है? (किमी/घंटा में)

A. 10 km/hr
B. 16 km/hr
C. 14 km/hr
D. 12 km/hr
E. 8 km/hr

Option “B” is correct.

Let the speed of boat be x km/hr

According to the question, 10/(x – 4) + 10/(x + 4) = 80/60

=> 10 (x + 4 + x – 4) = 4/3(x2 – 16)

=> 15x = x2 – 16

=>x2 – 16 – 15x = 0

=> x = 16, -1     (taking only positive value)

Therefore, the speed of boat in still water = 16km/hr

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