NCHMCT JEE 2018 Question Paper with solutions for online practice

Question : 16 of 200

Marks: +1, -0

In a stream running at 2 km/hr, a motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water.

18 km/hr
20 km/hr
22 km/hr
24 km/hr

Validate

Solution:

Let the speed of the motor boat = x km/hr
According to the question,

{10}/{x-2}+{10}/{x+2}={55}/{60}={11}/{12}

⇒{10[x+2+x-2]}/{(x-2)(x+2)} ={11}/{12}

⇒{20 x}/{x^{2}-4}=\;{11}/{12}

⇒11 x^{2}-44=240 x

⇒ 11 x^{2}-240 x-44=0

⇒11 x^{2}-242 x+2 x-44=0

⇒11 x(x-22)+2(x-22)=0

⇒(x-22)(11 x+2)=0

⇒x=22

x=-\;{2}/{11}

Hence, speed of the motor boat = 22 km/hr

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