# 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)

- 5
- 25/6
- 9/2
- 23/6

**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.