Driving his car at the speed of 30 km/h Vinod reached his office 5 min late. If his speed is 40 km/h, he reached the office 3 min early. Find the distance he travels between his residence and his office.

Correct option is A

Given:

Driving his car at the speed of 30 km/h Vinod reaches his office 5 min late and at speed of 40 km/h, he reaches the office 3 min early.

Formula used:

Time = $$\frac{Distance}{Speed}$$​​

Solution:

Let the time be ‘t’ minutes  to reach office

Let the distance be D.

Time for 30km/h

=> (t + 5)/60 = D/30      ----(1)      (1 minute = 1/60 hours)

Time for 40 km/h

=> (t – 3)/60 = D/40      ----(2)

Subtract equation (2) from (1)

=> [t + 5 - (t - 3)]/60 = D/30 - D/40

=> (D/30) - (D/40) = 8/60

=> (4D - 3D)/120 = 8/60

=> D/120 = 8/60

=> D = 16 km

Alternate Solution:

Difference in time = $$\frac{Distance}{Speed}$$​​

=> [5 + (-3)]/60 = D/30 – D/40    (8 minutes = 8/60 in hours)

=> 8/60 = D/30 – D/40 

=> D/120 = 8/60

 D = 16 km.

Hence, option (a) is the correct answer.