81. The speed of boat in still water is 27 kmph and the speed of the stream is 3 kmph. If the boat takes 2 hours more in upstream than in downstream for the same distance, then find the distance covered in downstream?

स्थिर जल में नाव की गति 27 किमी/घंटा है और धारा की गति 3 किमी/घंटा है। यदि नाव धारा के प्रतिकूल समान दूरी के लिए धारा के अनुकूल से 2 घंटे अधिक लेती है, तो धारा के अनुकूल तय की गई दूरी ज्ञात कीजिए?

A. 240 km
B. 280 km
C. 320 km
D. 360 km
E. None of these

Option “A” is correct.

The speed of boat in still water = 27 kmph

The speed of the stream = 3 kmph

Upstream speed = speed of boat in still water – speed of the stream

=> 27 – 3 = 24 kmph

Downstream speed = speed of boat in still water + speed of the stream

=> 27 + 3 = 30 kmph

(d/24) – (d/30) = 2 (according to the question)

d/(120) = 2

Distance = 240 km

82. A boat can cover 9.6 km upstream in 24 minutes. If the speed of the current is 1/4th of the boat in still water, then how much distance (in km) can the boat cover downstream in 36 minutes?

एक नाव 24 मिनट में धारा के प्रतिकूल 9.6 किमी की दूरी तय कर सकती है। यदि स्थिर जल में धारा की गति नाव की गति का 1/4 है, तो नाव धारा के अनुकूल 36 मिनट में कितनी दूरी (किमी में) तय कर सकती है?

A. 36 km
B. 24 km
C. 48 km
D. 32 km
E. None of these

Option “B” is correct.

Speed of upstream= (9.6 *60) / 24 = 24 km/hr

The speed of the current is 1/4th of the boat in still water.

= > Speed of current: Speed of still water = 1:4

Speed of upstream= Speed of still water- speed of Current

24= 3x =>x=8

Speed of current = 8 km/hr

Speed of boat in still water= 32 km/hr

Speed of downstream= Speed of still water + speed of Current

= > 32+8 = 40 km/hr

Here speed= 40 km/hr, Time= 36 minutes

Distance= 40 *(36/60) = 24 km

83. A boat took 12 hours less to travel a certain distance downstream than to travel the same distance upstream. If the speed of a boat in still water is 20 km/hr and speed of a stream is 12 km/hr, then find the total distance travelled by boat in downstream?

एक नाव धारा के अनुकूल एक निश्चित दूरी तय करने में धारा के प्रतिकूल समान दूरी तय करने में लिए समय से 12 घंटे कम लेती है। यदि स्थिर जल में एक नाव की गति 20 किमी/घंटा है और धारा की गति 12 किमी/घंटा है, तो नाव द्वारा धारा के अनुकूल तय की गई कुल दूरी ज्ञात कीजिए ?

A. 112 km
B. 140 km
C. 128 km
D. 156 km
E. None of these

Option “C” is correct.

Let the total distance be x,

Speed of downstream = 20 + 12 = 32 km/hr

Speed of upstream = 20 – 12 = 8 km/hr

According to the question,
12 = (x/8) – (x/32)

12 = (4x – x)/32

(12 * 32) = 3x

x = (12 * 32) / 3 = 128 km

The total distance travelled by boat = 128 km

84. A Boat takes 4.5 hours less to travel to 144 Km downstream than to travel the same distance upstream. If the speed of the stream is 8 Km/hr, then find the speed of boat in still water?

एक नाव धारा के अनुकूल 144 किमी की यात्रा करने में धारा के प्रतिकूल समान दूरी तय करने की तुलना में 4.5 घंटे कम लेती है। यदि धारा की गति 8 किमी/घंटा है, तो स्थिर जल में नाव की गति ज्ञात कीजिए?

A. 16 km/hr
B. 28 km/hr
C. 24 km/hr
D. 20 km/hr
E. None of these

Option “C” is correct.

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

According to the question,

[144/(x – 8)] – [144/(x + 8)] = (9/2)

[(x + 8) – (x – 8)]/[x2 – 64] = (9/2) * (1/144)

(16/[x2 – 64]) = 1/32

x2 – 64 = 512

x2 = 576

x = 24

The speed of boat in still water = 24 km/hr

85. The boat travelled 80 km upstream in 16 hours and travelled 280 km downstream in 8 hours. If the boat and stream’s speed is increased by 5 kmph and 3 kmph respectively, then what is the time taken by the boat travelled 301 km in upstream and downstream?

नाव 16 घंटे में धारा के प्रतिकूल 80 किमी की यात्रा करती है और 8 घंटे में धारा के अनुकूल 280 किमी की यात्रा करती है। यदि नाव और धारा की गति में क्रमशः 5 किमी प्रति घंटे और 3 किमी प्रति घंटे की वृद्धि की जाती है, तो नाव द्वारा धारा के प्रतिकूल और धारा के अनुकूल 301 किमी की यात्रा करने में कितना समय लगता है?

A. 40 hours
B. 45 hours
C. 50 hours
D. 60 hours
E. Cannot be determined

Option “C” is correct.

Upstream speed = 80/16 = 5 kmph

Downstream speed = 280/8 = 35 kmph

Speed of the boat = (35 + 5)/2 = 20 kmph

Speed of stream = (35 – 5)/2 = 15 kmph

After increasing the boat = 20 + 5 = 25 kmph

Stream speed = 15 + 3 = 18 kmph

Required time = 301/(25 + 18) + 301/(25 – 18) = 7 + 43 = 50 hours

86. Upstream speed of a boat is 4Km/h less than its downstream speed and speed of the boat in still water is 12 Km/h. Time taken by the boat to go 210 Km downstream is what percent of the time taken by the boat to go 120 Km upstream?

एक नाव की धारा के प्रतिकूल गति उसकी धारा के अनुकूल गति से 4 किमी/घंटा कम है और स्थिर जल में नाव की गति 12 किमी/घंटा है। नाव द्वारा धारा के अनुकूल 210 किमी जाने में लिया गया समय, नाव द्वारा 120 किमी धारा के प्रतिकूल जाने में लगने वाले समय का कितना प्रतिशत है?

A. 125%
B. 110%
C. 120%
D. 105%
E. None of these

Option “A” is correct.

Let, speed of the boat in still water = a Km/h

And speed of the stream = b Km/h

(a + b) – (a – b) = 4

=> a + b – a + b = 4

=> 2b = 4

=> b = 4/2

=> b = 2 Km/h

a = 12 Km/h

Time taken by the boat to go 210 Km downstream = 210/(12 + 2)

= 210/14

= 15 hours

Time taken by the boat to go 120 Km upstream = 120/(12 – 2)

= 120/10

= 12 hours

Required percentage = 15/12 x 100 = 125%

87. The speed of the stream is 8 kmph. If the time taken by the boat travels 240 km upstream and downstream in 40 hours, then what is the difference between the time taken by upstream covers 84 km and downstream covers 180 km?

धारा की गति 8 किमी प्रति घंटा है। यदि नाव द्वारा 240 किमी धारा के प्रतिकूल और धारा के अनुकूल यात्रा करने में लिया गया समय 40 घंटे है, तो धारा के प्रतिकूल 84 किमी और धारा के अनुकूल में 180 किमी की दूरी तय करने में लगने वाले समय में कितना अंतर है?

A. 3
B. 4
C. 5
D. 6
E. None of these

Option “A” is correct.

Stream speed = 8 kmph

240/(8 + x) + 240/(x – 8) = 40

6 * (x – 8 + 8 + x) = x2 – 64

12x = x2 – 64 = > x2 – 12x – 64 = 0 = > (x – 16) (x + 4) = 0

x = 16 kmph

Upstream speed = 16 – 8 = 8 kmph

Downstream speed = 16 + 8 = 24 kmph

Required Time = 84/8 – 180/24 = 10.5 – 7.5 = 3 hours

88. A boat is running in upstream takes 4 hours to cover a certain distance, while it takes 3 hours to cover the same distance running downstream. What is the ratio between the speed of the boat in still water and speed of the current respectively?

एक नाव धारा के प्रतिकूल चल रही है, एक निश्चित दूरी को तय करने में 4 घंटे का समय लेती है, जबकि धारा के अनुकूल चलते हुए समान दूरी को तय करने में 3 घंटे का समय लेती है। स्थिर जल में नाव की गति और धारा की गति के बीच क्रमशः अनुपात क्या है?

A. 1: 7
B. 7: 1
C. 2: 3
D. 3: 2
E. None of these

Option “B” is correct.

Let the upstream speed be x kmph and the downstream speed be y kmph.

Distance covered in upstream = Distance covered in downstream

x * 4 = y * 3

=> y = 4/3 * x

Required ratio = (y + x)/2: (y – x)/2

= (y + x): (y – x)

= (4/3 * x + x): (4/3 * x – x)

= 7x: x

= 7: 1

89. If the time taken by the boat to cover a certain distance along with stream is 18 hours less than the time taken by the same boat covers the same distance against stream. If the ratio of the speed of boat in still water to stream is 3:1, then find the distance covered by the boat along with stream.

यदि नाव द्वारा धारा के अनुकूल एक निश्चित दूरी तय करने में लिया गया समय उसी नाव द्वारा धारा के प्रतिकूल समान दूरी को तय करने में लिए गए समय से 18 घंटे कम है। यदि स्थिर जल में नाव की गति से धारा की गति का अनुपात 3:1 है, तो नाव द्वारा धारा के अनुकूल तय की गई दूरी ज्ञात कीजिए।

A. 180 km
B. 240 km
C. 360 km
D. Cannot be determined
E. None of these

Option “D” is correct.

Speed of the boat = 3x

Speed of the stream = x

d/(3x – x) – d/(3x + x) = 18

d/2x – d/4x = 18

2d – d = 18 * 4x

d = 18 * 4x

90. If the speed of the boat in still water is 50% more than the speed of the stream and the total time taken by the boat covers a certain distance along with stream and against stream in 60 hours, then what is the time taken by the boat covers same distance in still water?

यदि स्थिर जल में नाव की गति धारा की गति से 50% अधिक है और नाव द्वारा धारा के अनुकूल और धारा के प्रतिकूल एक निश्चित दूरी तय करने में लिया गया कुल समय 60 घंटे है, तो नाव स्थिर जल में समान दूरी तय करने में कितना समय लेती है?

A. 16 hours 40 minutes
B. 15 hours 30 minutes
C. 17 hours 15 minutes
D. 14 hours 20 minutes
E. None of these

Option “A” is correct.

Speed of the stream = 2x

Speed of the boat in still water = 2x * 150/100 = 3x

Distance = d

d/5x + d/(3x – 2x) = 60

d/5x + d/x = 60

6d = 60 * 5x

d = 50x

Required time = 50x/3x = 16 hours 40 minutes

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