A boy walking at a speed of 20 km/hr reaches his school 30 minutes late.Next time he increases his speed by 5 km/hr but still reaches 10 minuteslate. What is the distance of the school from his house?

Sure, let's solve this step by step:

Step 1: Let's denote the distance between the boy's house and his school as 'd' km.

Step 2: The boy initially walks at a speed of 20 km/hr but is 30 minutes late. So, the time he should have taken to reach school on time is (time taken at 20 km/hr speed - 30 minutes). We know that time = distance/speed, so the time taken at 20 km/hr speed = d/20 hours. But we need to convert 30 minutes into hours because our speed is in km/hr. 30 minutes = 0.5 hours. So, the time he should have taken to reach school on time = d/20 - 0.5 hours.

Step 3: Next, the boy increases his speed by 5 km/hr, making his speed 25 km/hr. But he is still 10 minutes late. So, the time he should have taken to reach school on time is (time taken at 25 km/hr speed - 10 minutes). Time taken at 25 km/hr speed = d/25 hours. Converting 10 minutes into hours, we get 10 minutes = about 0.167 hours. So, the time he should have taken to reach school on time = d/25 - 0.167 hours.

Step 4: Since the time to reach school on time should be the same in both cases, we can set the two times equal to each other and solve for 'd':

d/20 - 0.5 = d/25 - 0.167

Step 5: Solving this equation for 'd', we get:

d = 10 km

So, the distance of the school from his house is 10 km.