A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is

A) âˆš6 / âˆš2

B) âˆš7 / 2

C) 2âˆš5 / 3

D) 3: 2

Option (B)

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Time Speed Distance, we can see that

Total travel time gets reduced by 75%. So, total travel time becomes 1/4th of the original.

So, sâ€™(New speed) = 4s(Original speed)

Speed of boat : Speed of river = x:1

When the speed of boat is normal

Speed Upstream = x-1

Speed Downstream = x+1

Here, the distance is constant. So, average speed can be found out by the harmonic mean of two speeds = 2ab/ (a+b)

Here, average speed will be 2(x^2-1)/2x = (x^2-1)/x

When the speed of boat is doubled

Speed upstream = 2x-1

Speed downstream = 2x+1

Here, the distance is constant. So, average speed can be found out by the harmonic mean of two speeds = 2ab/(a+b)

Here, average speed will be 2(4x^2-1)/4x = (4x^2-1)/2x

Now, we know that

New speed = 4*Original speed

So,

(4x^2-1)/2x = 4(x^2-1)/x

4x^2 â€“ 1 = 8x^2 â€“ 8

4x^2 = 7

x = âˆš7/2

Ratio = x:1 = âˆš7/2

Option (B)

Quantitative Aptitude – Arithmetic – Time, Speed and Distance – Q1: A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike.

Quantitative Aptitude – Arithmetic – Time, Speed and Distance – Q2: Arun drove from home to his hostel at 60 miles per hour. While returning home he drove halfway along the same route at a speed of 25 miles per hour

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