Manoj travelled one third of a distance at an average speed of 16 km/hr then half of distance at a speed of 15Km/hr and covered the rest of distance at an average speed of 20km/hr. If he took total of 15 hours in completing the journey then total distance covered by him is​ ?

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Question

Manoj travelled one third of a distance at an average speed of 16 km/hr then half of distance at a speed of 15Km/hr and covered the rest of distance at an average speed of 20km/hr. If he took total of 15 hours in completing the journey then total distance covered by him is​?

a)  205 Km

b)  190 Km

c)   240 Km

d)  250 Km

Solution

Let's take total distance travelled in parts are 6
We have to find here Average Speed = Total distance travelled / Total time taken

Total distance travelled in parts are 6
Total time taken = distance_1/speed_1 + ....

1st one is 1/3rd of distance which is 1/3rd of 6 = 2 at speed of 16km/h
2nd one is 1/2 of distance which is 1/2 of 6 = 3     at speed of 15km/h

Average Speed = 6/ (2/16 + 3/15 + 1/20)
              = (6/15)*40

We have Average Speed now & total time also A.T.Q = 15 hours

So Total distance = Average Speed * Total time
                  = (6/15)*40     * 15
                  = 6*40*15/15
                  = 6*40
                  = 240 Km
Ans = 240 Km