CAT Question Bank  Time, Speed & Distance

@rowdyrathore could you explain how did you solve it?

@abhisd
Let the total distance b/w home and school be d, and the point they meet (say M) is at a distance x from the school. Let t be the time taken to cover distance d if they travel in car. We will take speed of car as s and walking speed as (s/6).
[H] < (d  x) >< [M] >< x > [S]
we know, d/s = t  (1)
In the given situation, son walked till M (distance of x) and father drove a distance of (d  x) after they meet. And they reached 30 minutes late by doing so. Remember 10 min was lost in waiting, so 20 mins was lost while travelling.
so, x/(s/6) + (d  x)/s = t + 20
6x/s + d/s  x/6 = t + 20
5x/s + d/s = t + 20  (2)
(2)  (1) = 5x/s = 20
x = 4s
So to cover distance x by walking it will take x/(s/6) = 4s/(s/6) = 24 minutes. Car would take 24/6 = 4 minutes to cover this part and hence car has saved 4 + 4 = 8 minutes (onward and return) because of the son walking this part.
Total time lost = Time lost in repair  Time saved by walking
30 minutes = Time lost in repair  8
Time lost in repair = 38 minutes.Alternatively, a much faster thought process by Chandra sir (Takshzila)
If son walked for 6t minutes, then the meeting of car and son happens at (10 + 6t) mins past 5:00 am.
In the event of no fault, car would have been at same point, going back, at t mins past 7:00 am.
Thus, (10 + 6t)  t = 30 i.e. t = 4
The bus is 30 mins late after having saved 4 + 4 = 8 mins by not travelling the distance walked by students.
Repair took 38 minutes.


@rowdyrathore 8km

9 hours...................................

5.....................................................

d ..............70

@rowdyrathore 20hours is the time.

@rowdyrathore please post the answer.I am confused between 27 and 24.what is the answer?


@manaswini Rohan's speed is 9 times than sohan.. so when Sohan completes 3 rounds, Rohan completes 3 * 9 = 27 rounds. 27 times ?