To find the speed of the bicycle, we can use the concept of relative speed.

Let's assume the speed of the bicycle is 'x' km/hr.

Speed of the wind is given as 10 km/hr.

When the man is cycling against the wind, his effective speed will be the difference between the speed of the bicycle and the speed of the wind. So, the effective speed against the wind will be (x - 10) km/hr.

When the man is cycling with the wind, his effective speed will be the sum of the speed of the bicycle and the speed of the wind. So, the effective speed with the wind will be (x + 10) km/hr.

We are given that the man covers a distance of 60 km in the direction of the wind and comes back to his original position in a total of 8 hours.

Let's break down the journey into two parts:

1. Cycling with the wind:
The time taken to cover a distance of 60 km with the wind can be calculated using the formula:
Time = Distance / Speed
So, the time taken to cover 60 km with the wind will be:
Time with the wind = 60 / (x + 10) hours

2. Cycling against the wind:
The time taken to cover a distance of 60 km against the wind can be calculated using the formula:
Time = Distance / Speed
So, the time taken to cover 60 km against the wind will be:
Time against the wind = 60 / (x - 10) hours

According to the given information, the total time taken for the journey is 8 hours:
Time with the wind + Time against the wind = 8

Substituting the values of Time with the wind and Time against the wind, we get:
60 / (x + 10) + 60 / (x - 10) = 8

To solve this equation, we can first find the common denominator:
[(x + 10)(x - 10)]

Multiplying both sides of the equation by [(x + 10)(x - 10)], we get:
60(x - 10) + 60(x + 10) = 8(x + 10)(x - 10)

Simplifying the equation, we get:
60x - 600 + 60x + 600 = 8(x^2 - 100)

Combining like terms, we get:
120x = 8x^2 - 800

Rearranging the equation, we get:
8x^2 - 120x - 800 = 0

Dividing both sides of the equation by 8, we get:
x^2 - 15x - 100 = 0

Now, we can solve this quadratic equation using factorization, completing the square, or the quadratic formula.

After solving the equation, we find that the speed of the bicycle is approximately 25 km/hr.

Therefore, the speed of the bicycle is 25 km/hr.

A man comes back to its original position.So distance of coming to the original position=60km/hNow the man comes back against the direction of wind .Now he comes back in 8 hours.So speed of bicycle=distance/time +10=60/8 +10=7.5+10=17.5 km/h.