A man travels from his home to the office at 4km/hr and reaches his office 20 min late. If the Speed had been 6 km/hr he would have reached 10 min early. Find the distance from his home to office?

Let,
The distance between home and office =d
Suppose he reaches the office on Time,
the Time taken = a minutes
Case 1: When he reaches office 20 minutes late,
Time taken = a + 20
Case 2: When he reaches office 10 minutes early,
Time taken = a - 10
As the distance traveled is the same,
The ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases.
Ratio of Speed in both cases = 4:6
= 2:3
Ratio of Time in both cases = 3:2
Therefore,
(a + 20)/(a -10)= 3/2
⇒ 2a + 40 = 3a -30
⇒ 3a - 2a = 40 + 30
⇒ a = 70 minutes.
Taking case 1,
4= d/(90/60)
⇒ d= 360/60
= 6 km.