If he reduces his speed by 1/5th, he goes 5 km less in the same time

A cyclist reaches a certain place in 6 hours. If he reduces his speed by  1/5th, he goes 5 km less in the same time. His speed (in km/hour)

  1. 5
  2. 25/6
  3. 9/2
  4. 23/6
Anurag Mishra Professor Asked on 20th April 2016 in Maths.
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1 Answer(s)

Answer: (2) 25/6 

Solution:-
Let the distance and  speed be X km and Y hr.

A cyclist reaches a certain place in 6 hrs.
Then,  X/Y = 6
X = 6 Y …………………………………. (1)

If he reduces his speed by 1/5th, he goes 5 km less in the same time.
Then,  (X – 5)/(4 Y/5) = 6
5 (X – 5)/ 4 Y = 6
From equation (1).
5 (6 Y – 5)/4 Y = 6
By cross multiplication,
5 (6 Y – 5) = 24 Y
30 Y – 25 = 24 Y
30 Y – 24 Y = 25
6 Y = 25
Y = 25/6

Then, the speed of the cyclist is 25/6.

Hence, the correct answer is option (2) 25/6.

Anurag Mishra Professor Answered on 24th April 2016.
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