1 Answers
Option 1 : 7.5 km
Given:
The man's initial speed was 10 km/h
For 10 km/h he reached the office 5 minutes late.
His final speed was 15 km/h
For 15 km/h he reached the office 10 minutes earlier.
Formula used:
Distance = (Speed × Time)
Calculation:
Let the distance be D
The difference between the time = {10 - (-5)}
⇒ 15 minutes
According to the question, we can say that {(D/10) - (D/15)} = (15/60) hours
⇒ (D/30) = (15/60)
⇒ D = (15/2)
⇒ D = 7.5
∴ The distance between his home and office is 7.5 km.
Shortcut Trick
Formula used:
Required distance = (Total time × Product of the two speeds)/Difference of the two speeds
Calculation:
Total time = {10 - (-5)} minutes
⇒ 15 minutes = 1/4 hours
Product of two speeds = (10 × 15) km/h
⇒ 150 km/h
Difference of the two speed = (15 - 10) hours
⇒ 5 hours
Distance = {(1/4) × (150/5)}
⇒ 7.5
∴ The distance between his home and office is 7.5 km.
Mistake Points
When two opposite terms used i.e., a person reaches one time early and another time late then always add the times.
When two same terms used i.e., a person reaches both of the time late or both of the time early then take the difference between them.