Question

Pratik takes 8 hours to travel 36 km downstream and return to the same spot the speed of boat in still water is 12 kilometre per hour find the speed of water current

Answer 1

Let the speed of the current be x km/hr.

Pratik goes 36 km downstream. 
∴ Distance covered by the Pratik in Downstream = 36 km.
Speed of the Pratik in downstream = (12 + x) km/hr.

∴ Time taken = 36/(12 + x)

Now, He also returned to the same spot.
∴ Distance covered in upstream = 36 km.
Speed of the Pratik in upstream = (12 - x) km/hr. 

∴ Time taken = 36/(12 - x)

Now,  
Time taken in upstream + Time taken in downstream = 8 hrs.
∴ 36/(12 - x) + 36/(12 + x) = 8
⇒ 36(12 + x) + 36(12 - x) = 8(12 + x)(12 - x)
⇒ 36(12 + x + 12 - x) = 8(144 - 12x + 12x - x²)
⇒ 36(24) = 8(144 - x²)
⇒ 36 × 3 = 144 - x²
∴ x² = 144 - 108
∴ x² = √36
⇒ x = +6 or -6

-6 cannot be possible.
∴ Speed of the current is 6 km/hr.



Hope it helps.

Answer 2

$\large{\mathbf{{HELLO \: \: DEAR,}}}$

$\mathbf{Let \: \: the \: \: speed \: \: of \: \: the \: \: current \: \: be \: \: x km/hr.} \\ \\ \mathit{\underline{NOW}} \\ \\ \mathit{( 1 ) CASE } \\ \\ \mathit{PRATIK \: \: GOES \: \: 36 KM \: \: DOWNSTREAM}\\ \\ \mathit{DISTANCE \: \: COVERED \: \: BY \: \: THE \: \: PRATIK \: \: IN DOWNSTREAM = 36 km}\\\\ \mathit{SPEED \: \: IN \: \: DOWNSTREAM = (12 + x) km/hr.} \\ \\ \mathit{Time \: \: taken = 36/(12 + x)}$

$( 2 ) CASE , \\ \\ \mathit{HE \:\: RETURNED \:\:TO \: \: THE \: \: SAME \: \: SPOT}\:\: \\ \\\mathit{DISTANCE \:\:COVERED\:\: IN \: \: UPSTREAM = 36 km} \\\\ \mathit{ SPEED \: \: IN \: \: UPSTREAM = (12 - x) km/hr}TIME \: \: TAKEN = 36/(12 - x) \\ \\ \mathbf{\underline{Now,}} \\ \\ \mathit{TIME \: \: TAKEN \: \: IN \: \: UPSTREAM \: + \: TIME \: \: TAKEN \: \: IN \: \: DOWNSTREAM = 8 hrs.} \\\\\frac{36}{(12 - x)} + \frac{36}{(12 + x)} = 8\\ \\ \mathit{\frac{36(12 + x) + 36(12 - x)}{(12 + x)(12 - x)}= 8}\\ \\ \\ \frac{12 + x + 12 - x}{144 - x^2}=\frac{8}{36}\\ \\ \frac{24}{144 - x^2}=\frac{2}{9}\\ \\ 216=288 - 2x^2\\ \\ 2x^2 = 288 - 216\\ \\ x^2 = \frac{72}{2}\\ \\ x^2 = 36 \\ \\ x= \sqrt{36} \\ \\ x = +_ - 6 \\ \\ or x = +6 \: , \: \: x = -6, \\ \\ x = -6 \: \: [ NEGLECT]$

$\mathit{HENCE, \: \: SPEED \: \: OF \: \: THE \: \: CURRENT \: \: IS \: \: 6 Km/hr.}$

$\large{\mathit{\underline{ I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR , \: \: THANKS}}}$