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Directions : Study the following information carefully and answer the questions given beside.
 
Fishes are one of the very few aquatic creatures that can easily swim against the flow of the current of a river. The Dolphin is a fish that swims in the waters of Brahmaputra River. Speed of Dolphin in still water is 80 km/h. However, it takes thrice the time to travel upstream than it takes to travel downstream. 
 
1
Find the speed of Dolphin when it is travelling upstream.
» Explain it
B
Let the speed of river be x

Speed of Dolphin upstream = 80 – x

Speed of Dolphin downstream = 80 + x

Let the distance travelled be Y

Then,

⇒  3Y  =  Y
80 + x 80 – x

⇒  3  =  1
80 + x 80 – x

⇒ 80 + x = 3(80 – x)

⇒ 80 + x = 240 – 3x

⇒ 4x = 160

⇒ x = 40

∴ Speed of Dolphin upstream = 80 – 40 = 40 km/h

Hence, option B is correct.
2
Find the ratio of speed of Dolphin downstream to its speed in still water.
» Explain it
C
Let the speed of river be x

Speed of Dolphin upstream = 80 – x

Speed of Dolphin downstream = 80 + x

Let the distance travelled be Y

Then,

⇒  3Y  =  Y
80 + x 80 – x

⇒  3  =  1
80 + x 80 – x

⇒ 80 + x = 3(80 – x)

⇒ 80 + x = 240 – 3x

⇒ 4x = 160

⇒ x = 40

∴ Speed of Dolphin downstream = 80 + 40 = 120km/h

∴ Ratio of speed downstream to speed in still water = 120 : 80 = 3 : 2

Hence, option C is correct.
3
Find the time taken by Dolphin to travel 8km upstream?
» Explain it
B
Let the speed of river be x

Speed of Dolphin upstream = 80 – x

Speed of Dolphin downstream = 80 + x

Let the distance travelled be Y

Then,

⇒  3Y  =  Y
80 + x 80 – x

⇒  3  =  1
80 + x 80 – x

⇒ 80 + x = 3(80 – x)

⇒ 80 + x = 240 – 3x

⇒ 4x = 160

⇒ x = 40

∴ Speed of Dolphin upstream = 80 – 40 = 40 km/h

∴ Time to travel 8km upstream

8  =  1  hours = 12 minutes
40 5

Hence, option B is correct.
4
Find the time taken by Dolphin to travel 40km downstream ?
» Explain it
A
Let the speed of river be x

Speed of Dolphin upstream = 80 – x

Speed of Dolphin downstream = 80 + x

Let the distance travelled be Y

Then,

⇒  3Y  =  Y
80 + x 80 – x

⇒  3  =  1
80 + x 80 – x

⇒ 80 + x = 3(80 – x)

⇒ 80 + x = 240 – 3x

⇒ 4x = 160

⇒ x = 40

∴ Downstream Speed of Dolphin = 80 + 40 = 120 km/h

∴ Time to travel 40km downstream

40  =  1  hours = 20 minutes
120 3

Hence, option A is correct.
5
Find the ratio of downstream speed to upstream speed of Dolphin.
» Explain it
D
Let the speed of river be x

Speed of Dolphin upstream = 80 – x

Speed of Dolphin downstream = 80 + x

Let the distance travelled be Y

Then,

⇒  3Y  =  Y
80 + x 80 – x

⇒  3  =  1
80 + x 80 – x

⇒ 80 + x = 3(80 – x)

⇒ 80 + x = 240 – 3x

⇒ 4x = 160

⇒ x = 40

∴ Downstream speed of Dolphin = 80 + 40 = 120 km/h

And upstream speed of Dolphin = 80 – 40 = 40 km/h

∴ Required ratio = 120 : 40 = 3 : 1

Hence, option D is correct.