A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is

To find the distance, we use the relationship between speed, time, and distance. Let the distance be D. The time taken at 5 km/hr is D divided by 5, and the time taken at 6 km/hr is D divided by 6. The difference between being 3 minutes late and 7 minutes early is a total of 10 minutes. Converting this to hours, we get 10 divided by 60, which is 1 divided by 6 hours. The equation is: D/5 minus D/6 equals 1/6. To solve this, find a common denominator for the left side, which is 30: 6D/30 minus 5D/30 equals 1/6. D/30 equals 1/6. Multiplying both sides by 30 gives: D equals 30 divided by 6. D equals 5 km. Therefore, the distance of the factory from his house is 5 km. The correct option is B.