1. A man rows a boat from point A against current for 10 minutes and then comes back with the current for next 10 minutes and reaches to a point B. if distance between A and B is 1 km, find the speed of the current.A1 km/hB2 km/hC2.5 km/hD3 km/h

To solve this problem, we need to understand that the speed of the current affects the man's speed when he is rowing against it and with it.

Step 1: Let's denote the speed of the man in still water as 'v' km/h and the speed of the current as 'c' km/h.

Step 2: When the man is rowing against the current, his effective speed is (v-c) km/h. Since he rows for 10 minutes, the distance he covers is Distance1 = Speed * Time = (v-c) * 10/60 km.

Step 3: When the man is rowing with the current, his effective speed is (v+c) km/h. Since he rows for 10 minutes, the distance he covers is Distance2 = Speed * Time = (v+c) * 10/60 km.

Step 4: The total distance covered by the man is the sum of Distance1 and Distance2, which is given as 1 km. So, we have the equation: (v-c) * 10/60 + (v+c) * 10/60 = 1.

Step 5: Solving this equation, we find that v = 3 km/h.

Step 6: However, we are asked to find the speed of the current 'c'. We can use either Distance1 or Distance2 to find this. Let's use Distance1: (v-c) * 10/60 = Distance1. Substituting the values, we get: (3-c) * 10/60 = 0.5.

Step 7: Solving this equation, we find that c = 2 km/h.

So, the speed of the current is 2 km/h. The answer is B. 2 km/h.