111. The upstream speed of the boat is 60% of the downstream speed of the boat. If the time taken by a boat traveling a distance of 225 km upstream is 2 hours more than that of downstream, then find the time taken by the boat traveling a distance of 180 km in still water?

नाव की ऊर्ध्वप्रवाह गति, नाव की अनुप्रवाह गति का 60% है। यदि एक नाव द्वारा ऊर्ध्वप्रवाह 225 किमी की दूरी तय करने में लिया गया समय अनुप्रवाह तय करने में लिया गया समय से 2 घंटे अधिक है, तो शांत पानी में 180 किमी की दूरी तय करने वाली नाव द्वारा लिया गया समय ज्ञात कीजिए?

A. 2 hours
B. 7 hours
C. 5 hours
D. 3 hours
E. None of these

Option “D” is correct.

The ratio of upstream and downstream speed of the boat=60:100=3:5

The downstream speed of the boat =5X

The upstream speed of the boat =3X

(225/3X)-(225/5X)=2

75/X-45/X=2

30=2X

X=15

The downstream speed of the boat=15*5=75 kmph

The upstream speed of the boat=15*3=45 kmph

The speed of the boat in still water=(75+45)/2=60 kmph

Required time=180/60=3 hours

112. Upstream speed is 62.5% of the speed of the boat in still water. If the speed of the current is 25 kmph less than the speed of the boat in still water, then what is the distance covered by the boat along with stream in 7 hours?

ऊर्ध्वप्रवाह गति, शांत जल में नाव की गति का 62.5% है। यदि धारा की गति, शांत जल में नाव की गति से 25 किमी प्रति घंटे कम है, तो 7 घंटे में नाव धारा के साथ कितनी दूरी तय करती है?

A. 350 km
B. 399 km
C. 385 km
D. 420 km
E. 434 km

Option “C” is correct.

Speed of boat = 8x

Speed of upstream = 8x * 62.5/100 = 5x

8x-(8x-5x) = 25

x = 5

Speed of boat = 8 * 5 = 40 kmph

Speed of current = 8x – 5x = 3 * 5 = 15 kmph

Required distance = 7 * (15 + 40) = 385 km

113. The speed of a boat in downstream is 4/3 times the speed of the boat in upstream. The speed of the current is what percentage of the speed of the boat in still water?

अनुप्रवाह में नाव की गति ऊर्ध्वप्रवाह में नाव की गति का 4/3 गुना है। धारा की गति स्थिर पानी में नाव की गति का कितना प्रतिशत है?

A. 12%
B. 14.28%
C. 19%
D. 27%
E. None of these

Option “B” is correct.

Let us take the speed of boat and speed of stream be x and y respectively.

(x + y) = 4/3 * (x – y)

=> y = x/7

= > x/y = 7: 1

Required percentage = 1/7 * 100 = 14.28%

114. Time taken by the boat in upstream is thrice of the time taken by it in downstream, but the distance covered by it in upstream is only 60% of the distance covered by it downstream. Find the ratio of the speed of the boat in still water to the speed of the current?

नाव द्वारा ऊर्ध्वप्रवाह में लिया गया समय उसके अनुप्रवाह में लगने वाले समय का तीन गुना होता है, लेकिन ऊर्ध्वप्रवाह में उसके द्वारा तय की गई दूरी उसके अनुप्रवाह में तय की गई दूरी का केवल 60% होती है। स्थिर पानी में नाव की गति से धारा की गति का अनुपात ज्ञात कीजिये?

A. 2:1
B. 3:2
C. 4:3
D. 5:4
E. 6:5

Option “B” is correct.

Speed of the boat = x

Speed of the stream = y

Distance covered in downstream = d

(d*60/100) / (x – y) = 3 * ( d / (x + y) )

0.6/(x-y) = 3/(x+y)

5x – 5y = x + y

4x = 6y

x/y = 3/2

115. The time taken by the boat to travel 360 km distance downstream is 60% of the time taken to travel the same distance upstream. If the speed of the stream is 5 kmph, then what is the speed of the boat in still water?

नाव द्वारा 360 किमी की दूरी की अनुप्रवाह यात्रा करने में लगने वाला समय, उसी दूरी के उर्धव्प्र्वाह पर जाने के लिए लिए गए समय का 60% है। यदि धारा की गति 5 किमी प्रति घंटा है, तो शांत जल में नाव की गति क्या है?

A. 10 kmph
B. 12 kmph
C. 15 kmph
D. 20 kmph
E. 18 kmph

Option “D” is correct.

Speed of the boat in still water=x

360/(x + 5)=60/100 * (360/(x – 5))

5/(x + 5)=3/(x – 5)

3x + 15=5x – 25

2x=40

X=20 kmph

116. A boat running upstream covers a distance of 65 km in 13 hours and for covering the same distance downstream it takes 5 hours. Find the speed of the stream is what percentage of the downstream speed?(aprrox.)

एक नाव 13 घंटे में 65 किमी की ऊर्ध्वप्रवाह दूरी तय करती है और समान दूरी अनुप्रवाह में तय करने के लिए 5 घंटे लगते हैं। धारा की गति, अनुप्रवाह गति का कितना प्रतिशत है? (लगभग)

A. 34%
B. 31%
C. 25%
D. 28%
E. None of these

Option “B” is correct.

Upstream speed is = 65/13 = 5 km/hr

Downstream speed is = 65/5 = 13 km/hr

So, the speed of the stream is = (13 – 5)/2

= 8/2 = 4 km/hr

Thus, the required percentage is = 4/13 × 100 ≈ 31%

117. Ratio of speed of a boat in upstream to downstream is 1: 3. If the boat travels 24km in upstream and 48km in downstream in 2 hours, then the speed of stream is what percent of the speed of boat in still water?

ऊर्ध्वप्रवाह तथा अनुप्रवाह में एक नाव की गति का अनुपात 1 : 3 है। यदि नाव 2 घंटे में 24 किमी ऊर्ध्वप्रवाह और 48 किमी अनुप्रवाह यात्रा करती है, तो धारा की गति, स्थिर पानी में नाव की गति का कितना प्रतिशत है?

A. 50%
B. 40%
C. 30%
D. 20%
E. None of these

Option “A” is correct.

US = x kmph and DS = 3x kmph

24/x + 48/3x = 2

=> x = 20

US = 20 kmph and DS = 60kmph

Speed of boat in still water = (20 + 60)/2 = 40kmph

Speed of stream = (60 – 20)/2 = 20kmph

Required % = 20/40 * 100 = 50%

118. The speed of the stream is 33.33% of the speed of the boat in still water. If the total time taken by the boat to cover 240 km downstream and 150 km upstream in 9 hours, then find the time taken by the boat to cover 225 km in still water?

धारा की गति स्थिर जल में नाव की गति का 33.33 प्रतिशत है। यदि नाव द्वारा धारा के अनुकूल 240 किमी और धारा के प्रतिकूल 150 किमी की दूरी 9 घंटे में तय की जाती है, तो स्थिर जल में नाव द्वारा 225 किमी की दूरी तय करने में कितना समय लगता है?

A. 7 hours
B. 5 hours
C. 9 hours
D. 6 hours
E. None of these

Option “B” is correct.

Let the speed of boat=3x km/hr

And the speed of the stream=3x*1/3=x km/hr

240/(3x+x)+150/(3x-x)=9

240/4x+150/2x=9

60/x+75/x=9

135/9=x

x=15

Speed of the boat=3*15=45 km/hr

Required time=225/45=5 hours

119. The ratio between speed of current to speed of boat in still water is 2: 5. The downstream speed is what percent of the upstream speed?

शांत जल में धारा की गति से नाव की गति का अनुपात 2: 5 है। धारा-अनुकूल की गति, धारा-प्रतिकूल की गति का कितना प्रतिशत है?

A. 166 (2/3) %
B. 233 (1/3) %
C. Cannot be determined
D. 133 (1/3) %
E. 200 %

Option “B” is correct.

Speed of current = 2x

Speed of boat in still water = 5x

Therefore Downstream speed = 7x

Upstream speed = 3x

Required Percentage = (7x/3x)×100

Required Percentage = 233 (1/3) %

120. The time taken by the boat to travel 360 km distance downstream is 60% of the time taken to travel the same distance upstream. If the speed of the stream is 5 kmph, then what is the speed of the boat in still water?

नाव द्वारा 360 किमी की दूरी की अनुप्रवाह यात्रा करने में लगने वाला समय, उसी दूरी को उर्धव्प्रवाह तय करने के लिए लिए गए समय का 60% है। यदि धारा की गति 5 किमी प्रति घंटा है, तो शांत जल में नाव की गति क्या है?

A. 10 kmph
B. 12 kmph
C. 15 kmph
D. 20 kmph
E. 18 kmph

Option “D” is correct.

Speed of the boat in still water=x

360/(x + 5)=60/100 * (360/(x – 5))

5/(x + 5)=3/(x – 5)

3x + 15=5x – 25

2x=40       

x=20 kmph

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