Select the correct answerA person covers a certain distance with certain speed if he increases his speed by 15 km/hr. Then he will be 16 min. early. By how much time he will be late if he reduces his speed by 12 km/hr, if his initial speed is 60 km/hr?Options15 min25 min24 min20 min

To solve this problem, we need to understand the relationship between speed, distance, and time. The formula is Distance = Speed x Time.

1. First, let's find the distance covered by the person. We know that the initial speed is 60 km/hr and if the speed is increased by 15 km/hr, the person arrives 16 minutes early. So, the time taken at the increased speed is the original time minus 16 minutes.

   Let's denote the original time as 't' hours. Then, the time at the increased speed is (t - 16/60) hours, because we need to convert minutes to hours by dividing by 60.

   Therefore, the distance covered is Speed x Time = (60 + 15) km/hr x (t - 16/60) hours.

2. We also know that the same distance is covered at the original speed in 't' hours. So, we can set up the equation:

   60t = 75(t - 16/60)

   Solving this equation gives t = 1.2 hours, which is the original time taken to cover the distance.

3. Now, let's find out how late the person will be if the speed is reduced by 12 km/hr. The reduced speed is (60 - 12) = 48 km/hr.

   The time taken at the reduced speed is Distance / Speed = 60t / 48 = 1.2 hours / 48 km/hr = 1.5 hours.

4. Therefore, the person will be (1.5 - 1.2) hours = 0.3 hours late. Converting hours to minutes (by multiplying by 60), we get 0.3 x 60 = 18 minutes.

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