A worker reaches his work place 15 minutes late by walking at 4 kmph from his house. The next: day he increases his speed by 2 kmph and reaches in time. Find the distance from his house to his work place

3 km

Ratio of speed before and after increase:

S₁ : S₂ - 4 : 6

S₁ : S₂ - 2 : 3

Ratio of time is inversely proportional to that of speed because when speed increases time decreases and vice-versa. So, 

Ratio of time

T₁: T₂ - 3 : 2 

Difference between the time he reached with speed of 4 km/hr and 6 km/hr is 15 minutes. Thus, we can say value of 1 part is 15 minutes Thus, the actual time with speed 6km/hr is 30 minutes. As, we know that

Speed = \(\frac{ Distance}{ Time}\)

Distance = Speed x Time

Distance = 6 km/hr x \(\frac{ 1}{ 2}\) hr

Distance = 3 km