A boy walking at a speed of 20kmph reaches his school 15min late. Next time at a speed of 25kmph reaches his school 10m early find the usual time to reach the school?Options120min110min144min150min

Let's solve this step by step:

1. First, let's convert the speeds from km/h to km/min. This is done by dividing the speed by 60 (since there are 60 minutes in an hour). So, 20 km/h = 20/60 = 1/3 km/min and 25 km/h = 25/60 = 5/12 km/min.

2. Let's denote the distance to school as D (in km) and the usual time to reach the school as T (in minutes).

3. From the first sentence, we know that the boy covers the distance to school at a speed of 1/3 km/min and it takes him T+15 minutes. So, we can write the first equation: D = (1/3) * (T+15).

4. From the second sentence, we know that the boy covers the same distance at a speed of 5/12 km/min and it takes him T-10 minutes. So, we can write the second equation: D = (5/12) * (T-10).

5. Now we have a system of two equations with two variables (D and T). We can solve this system by equating the right sides of the equations:

(1/3) * (T+15) = (5/12) * (T-10)

6. To solve for T, first multiply through by 12 to get rid of the fractions:

4*(T+15) = 5*(T-10)

7. Expand both sides:

4T + 60 = 5T - 50

8. Rearrange to solve for T:

T = 110 minutes

So, the usual time to reach the school is 110 minutes. Therefore, the correct option is 110min.