A man travels from his home to office at 4 km/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.

Question: A man travels from his home to office at 4 km/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.

Solution:
Let the Distance between home and office = d.
Suppose he reaches the office on Time, the Time taken = x minutes

Case 1: When he reaches office 20 minutes late,
Time taken = x + 20 minutes

Case 2: when he reaches office 10 minutes early,
Time taken = x - 10 minutes

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

∴ (x + 20)/(x - 10) = 3/2
⇒ 2x + 40 = 3x -30
∴ x = 70

minutes Taking case 1,
70 + 20 minutes
= 90 minutes

In 60 minutes he reached 4000 m
∴ In 1 minutes he reached 4000/60 m
∴ In 90 minutes he reached (4000 × 90)/60 m
= 6000 m
= 6 km