Quantitative Aptitude – Arithmetic – TSD – A man travels by a motor boat
Quantitative Aptitude – Arithmetic – Time, Speed and Distance
Question
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) √6 / √2
B) √7 / 2
C) 2√5 / 3
D) 3: 2
Answer
Option (B)
Solution
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, s’(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 – 1 = 8x^2 – 8
4x^2 = 7
x = √7/2
Ratio = x:1 = √7/2
Option (B)
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