Question

A boy leave his home for school and walks at a speed of 10 km/h and reaches his school 15 minutes late. Next day boy started with a speed of 12 km/h and reaches his school 5 minutes earlier. Find the distance between his school and home.

1. 22 Kilometers
2. 24 Kilometers
3. 20 Kilometers
4. 18 Kilometers

Answer 1

Correct Answer - Option 3 : 20 Kilometers

Given:

Speed on Day 1 = 10 km/h

Time taken more than actual time = 15 minutes

Speed on day 2 = 12 km/h

Time taken less than actual time = 5 minutes

Formula Used:

Time = (Distance/Speed)

Concept Used:

In case 1 boy is 15 minutes late than actual time

In case 2 boy is 5 minutes earlier than actual time

Total time difference between the two times taken = 15 - (-5) = 20 Minutes

Calculation:

Let the distance between home and school be D

Time elapsed between two cases on 2 days = 20 Minutes

Difference between the times taken on 2 days = (D/10) – (D/12)

⇒ (D/10) – (D/12) = (20/60)

⇒ [(6D – 5D)/60] = (1/3)

⇒ (D/60) = 1/3

⇒ D = 20 kilometers

∴ The distance between Home and school is 20 kilometers