121. The downstream speed of the boat is two times the upstream speed of the boat. The boat covers 240 km downstream and 210 km upstream in 11 hours. If the speed of the boat in still water is decreased by 20%, then find the total distance covered by the boat in still water in 5 hours?

नाव की धारा के अनुकूल गति, नाव की धारा के प्रतिकूल गति की दुगुनी है। नाव 11 घंटे में 240 किमी धारा के अनुकूल और 210 किमी धारा के प्रतिकूल तय करती है। यदि स्थिर जल में नाव की गति 20% कम हो जाती है, तो स्थिर जल में नाव द्वारा 5 घंटे में तय की गई कुल दूरी ज्ञात कीजिए?

A. 300 km
B. 240 km
C. 450 km
D. 180 km
E. None of these

Option “D” is correct.

Upstream speed of the boat=x

Downstream speed of the boat=2x

240/2x+210/x=11

660=22x

x=30

Speed of the boat=(30+2*30)/2=45 kmph

Speed of the boat is decreased by 20%=45*80/100=36 kmph

Required distance=36*5=180 km

122. A boat covers 150 km upstream in 5 hours and the same boat covers 120 km in still water in 3 hours.If the speed of the boat in still water is increased by 5 km/hr, then find the downstream speed of the boat.

एक नाव 5 घंटे में धारा के प्रतिकूल 150 किमी की दूरी तय करती है और वही नाव स्थिर जल में 120 किमी 3 घंटे में तय करती है। यदि स्थिर जल में नाव की गति में 5 किमी/घंटा की वृद्धि कर दी जाती है, तो नाव की धारा के अनुकूल गति ज्ञात कीजिए।

A. 60 km/hr
B. 45 km/hr
C. 55 km/hr
D. 30 km/hr
E. None of these

Option “C” is correct.

The actual upstream speed of the boat = 150/5 = 30 km/hr

The actual speed of the boat in still water = 120/3 = 40 km/hr

The actual speed of the stream = 40 – 30 = 10 km/hr

The new speed of the boat in still water = 40 + 5 = 45 km/hr

Therefore, the new downstream stream speed of the boat = 45 + 10 = 55 km/hr

123. The sum of the speed of the boat in still water and stream is 18 kmph. If the speed of the boat in still water is decreased by 20% and the speed of stream is increased by 50%, then the boat takes to cover 225 km upstream in 30 hours, then find the speed of stream?

स्थिर जल में नाव और धारा की गति का योग 18 किमी प्रति घंटा है। यदि स्थिर जल में नाव की गति 20% कम हो जाती है और धारा की गति 50% बढ़ जाती है, तो नाव 30 घंटे में धारा के प्रतिकूल 225 किमी की दूरी तय करती है, तो धारा की गति ज्ञात कीजिए?

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

Option “A” is correct.

Speed of stream = x

Speed of boat in still water = 18 – x

225/((18 – x) * 80/100 – (x * 150/100)) = 30

7.5 * 100 = 1440 – 80x – 150x

x = 3 kmph

124. Ratio of the speed of the boat in still water to speed of stream is 4:1 and the boat covers 120 km upstream and downstream in 8 hours. If the speed of the boat in still water is increased by x km/hr and then the boat covers 200 km in still water in 5 hours, then find the value of x?

स्थिर जल में नाव की गति से धारा की गति का अनुपात 4:1 है और नाव धारा के प्रतिकूल और धारा के अनुकूल 120 किमी की दूरी 8 घंटे में तय करती है। यदि स्थिर जल में नाव की गति x किमी/घंटा बढ़ा दी जाती है और फिर नाव स्थिर जल में 200 किमी की दूरी 5 घंटे में तय करती है, तो x का मान ज्ञात कीजिए?

A. 12 km/hr
B. 8 km/hr
C. 10 km/hr
D. 16 km/hr
E. None of these

Option “B” is correct.

Let the speed of the boat = 4x

And the speed of the stream = 1x

120/(4x+1x) + 120/(4x-1x) = 8

120/5x + 120/3x = 8

24/x + 40/x = 8

64/8 = x

x = 8 km/hr

The speed of the boat in still water = 4 * 8 = 32 km/hr

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

x= 40 – 32 = 8 km/hr

125. Ratio of the speed of the boat and stream is 4:1 and the boat travels 252 km upstream in 7 hours. If the speed of the boat in still water is increased by 25%, then find the time taken by boat to cover 360 km downstream and 240 km upstream?

नाव और धारा की गति का अनुपात 4:1 है और नाव 7 घंटे में धारा के प्रतिकूल 252 किमी की यात्रा करती है। यदि स्थिर जल में नाव की गति में 25% की वृद्धि की जाती है, तो नाव द्वारा धारा के अनुकूल 360 किमी और धारा के प्रतिकूल 240 किमी की दूरी तय करने में कितना समय लगता है?

A. 10 hours
B. 7 hours
C. 9 hours
D. 8 hours
E. None of these

Option “A” is correct.

The upstream speed of the boat=252/7=36 km/hr

The speed of the boat=36*4/(4-1)=48 km/hr

The speed of the stream=48-36=12 km/hr

The speed of the boat in still water is increased by 25%=48*125/100=60 km/hr

New upstream speed of the boat=60-12=48 km/hr

New downstream speed of the boat=60+12=72 km/hr

Required time=360/72+240/48=5+5=10 hours

126. A boat covers 24km upstream and 20km downstream together in 7.25 hours. The ratio of the speed of the boat in still water to the speed of the stream is 5: 3. Find the time taken by boat to cover a distance of 38km in upstream, if the speed of the boat in still water is increased by 10%.

एक नाव 7.25 घंटे में एक साथ 24 किमी ऊर्ध्वप्रवाह और 20 किमी अनुप्रवाह को तय करती है। स्थिर पानी में नाव की गति तथा धारा की गति का अनुपात 5 : 3 है। ऊर्ध्वप्रवाह 38 किमी की दूरी तय करने के लिए नाव द्वारा लिया गया समय ज्ञात करें, यदि स्थिर पानी में नाव की गति 10% बढ़ जाती है।

A. 5 hours
B. 5.2 hours
C. 7 hours
D. 7.6 hours
E. None of these

Option “D” is correct.

Speed in still water = 5x and Stream speed = 3x

24/(5x – 3x) + 20/(5x + 3x) = 7.25

=> x = 2

Speed in still water = 10kmph and Stream speed = 6kmph

New speed in still water = 10 * 1.10 = 11kmph

Time taken = 38/(11 – 6) = 7.6 hours

127. A boat covers 150 km downstream in 2 hours 30 minutes and the same boat cover 120 km upstream in 3 hours. If the speed of the boat in still water is decreased by 20%, then find the time taken by the boat to cover 200 km downstream.

एक नाव धारा के अनुकूल 150 किमी की दूरी 2 घंटे 30 मिनट में तय करती है और वही नाव धारा के प्रतिकूल 120 किमी 3 घंटे में तय करती है। यदि स्थिर जल में नाव की गति 20% कम हो जाती है, तो नाव द्वारा धारा के अनुकूल 200 किमी की दूरी तय करने में लगने वाला समय ज्ञात कीजिए।

A. 2.5 hours
B. 8 hours
C. 4 hours
D. 5 hours
E. None of these

Option “C” is correct.

The upstream speed of the boat = 120/3 = 40 km/hr

The time taken by the boat to cover 150 km downstream in hours = 2.5 hours

The downstream speed of the boat = 150/2.5 = 60 km/hr

The speed of the boat in still water = (60 + 40)/2 = 100/2 = 50 km/hr

The speed of the stream in still water = 60 – 50 = 10 km/hr

The new speed of the boat in still water = 50 * (100 – 20)/100 = 50 * 80/100 = 40 km/hr

The new downstream speed of the boat = 40 + 10 = 50 km/hr

Required time = 200/50 = 4 hours

128. A boat covers 160 km downstream and 112 km upstream in 12 hours and the ratio of the speed of the boat in still water to the speed of the stream is 3:1. If the speed of the boat in still water is increased by 25%, then find the new downstream speed of the boat?

एक नाव धारा के अनुकूल 160 किमी और धारा के प्रतिकूल 112 किमी की दूरी 12 घंटे में तय करती है और स्थिर जल में नाव की गति से धारा की गति का अनुपात 3:1 है। यदि स्थिर जल में नाव की गति में 25% की वृद्धि की जाती है, तो नाव की धारा के अनुकूल नई गति ज्ञात कीजिए?

A. 36 km/hr
B. 54 km/hr
C. 38 km/hr
D. 42 km/hr
E. None of these

Option “C” is correct.

[160/(3x + x)] + [112/(3x – x)] = 12

160/4x + 112/2x = 12

40/x + 56/x = 12

x = 96/12

x = 8

The downstream speed of the boat = (3 + 1) * 8 =  4 * 8 = 32 km/hr

The upstream speed of the boat = (3 – 1) * 8 = 2 * 8 = 16 km/hr

The actual speed of the boat in still water = (32 + 16)/2 = 48/2 = 24 km/hr

The new speed of the boat in still water = 24 * 125/100 = 30 km/hr

The new downstream speed of the boat = 30 + 8 = 38 km/hr

129. A boat covers 120 km along with stream in x hours. Ratio of the speed of boat in still water to current is 3:1. If the speed of boat is increased by 20% and covers 92 km downstream in (x – 2) hours, then find the time taken by the boat covers 100 km against stream.

एक नाव x घंटे में धारा के साथ 120 किमी को तय करती है। ठहरे हुए पानी में नाव की गति से धारा की गति का अनुपात 3:1 है। यदि नाव की गति में 20% से वृध्दि की गई है और यह (x-2) घंटे में 92 किमी धारा-अनुकूल को तय करती है, फिर धारा के विरुद्ध 100 किमी को तय करने में नाव के द्वारा लिए गए समय को ज्ञात कीजिए।

A. 8 hours
B. 12.5 hours
C. 10 hours
D. 20 hours
E. None of these

Option “C” is correct.

Boat speed = 3a

Current speed = a

120/4a = x

30 = ax

92/((3a * 120/100) + a) = (x – 2)

20 = a (x – 2)

20 = ax – 2a

20 = 30 – 2a

a = 5

Speed of boat = 3 * 5 = 15

Required time = 100/(15 – 5) = 10 hours

130. A boat covers 264 km along the stream in 6 hours and the same boat covers 252 km against the stream in 9 hours. If the speed of the boat is increased by 16.67%, then find the time taken by the boat in still water to cover 336 km?

एक नाव 6 घंटे में धारा के साथ 264 किमी की दूरी तय करती है और वही नाव 9 घंटे में धारा के विपरीत 252 किमी की दूरी तय करती है। यदि नाव की गति में 16.67% की वृद्धि की जाती है, तो स्थिर जल में नाव द्वारा 336 किमी की दूरी तय करने में लिया गया समय ज्ञात कीजिए।

A. 8 hours
B. 3 hours
C. 6 hours
D. 7 hours
E. None of these

Option “A” is correct.

Downstream speed of the boat=264/6=44 kmph

Upstream speed of the boat=252/9=28 kmph

Speed of the boat=(28+44)/2=36 kmph

Speed of the boat is increased by 16.67%=36*7/6=42 kmph

Required time=336/42=8 hours

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