Finding The Average Speed

A man drives his car to the office at 20miles/hr. After reaching the office, he realizes that it's a new year holiday so he went back home at a speed of 30miles/hr.

Discounting the time spent in the stoppage what was his average speed of his journey?

Right way to calculate the average speed! 

Source 

Right Way To Find The Average Speed

What was the given data?

If you are finding average speed of 2 given speeds as (Speed 1 + Speed 2)/2 then you are getting tricked by questioner. The speed itself is a distance covered per unit i.e. Speed = Distance/Time. Calculating average speed like that means,you are doing like,

Average Speed = (Speed1 + Speed2)/2
                     
                      = (Distance1/Time1 + Distance 2/Time2)/2              
            
So you need to find the total distance traveled & the total time taken to complete the entire journey.It should be like,


Average Speed = Total Distance/Total Time

                       = (Distance1 + Distance2)/(Time1 + Time2)

In the given problem, let D be the distance traveled by car to the office. Let T1 be the time required to go to the office & T2 be the time to return back.

Since, Speed = Distance / Time, Time = Distance / Speed.

Hence, 

T1 = D / 20

T2 = D / 30

Now,

Total distance traveled =  D + D = 2D, Total Time taken = T1 + T2

Hence,

Average Speed = 2D / (T1 + T2)

Average Speed = 2D / (D/20 + D/30)

Average Speed = 2D / (50D/600)

Average Speed = 2D / (D / 12)

Average Speed = 24 miles/hr.  

Therefore, the average speed of the journey is 24 miles/hr not 25 miles/hr [(20 + 30)/2].

  
 

Guess The Order Of Cards

A man sitting opposite you has four cards in his hand facing him: 2, 3, 4 and 5 (but not in that order). He wants them placed in ascending order from his left to his right. To do this, he takes the leftmost card (from your perspective) and puts it last. He then takes the third card from the right (your right) and puts it in the last place.

What was the previous order of the cards?

Order Of Cards?

Here was the previous order! 

Source 

Identified The Order of The Cards

How cards were shuffled? 

Since he puts the leftmost card (from our point of view) to it's opposite location that card must be 2 (that's the smallest one & needs to be first in ascending order).

So the last card (from his point of view) must be 2. We still don't know exact positions of 3,4,5. Now 2 is in first position

Now what he does is that, moves third card from his left (our right) to the last position. Now to be in ascending order the last card must be 5. So the card that he used in this move must be 5.

Since these 2 moves completes the ascending order, rest must be in ascending from left to right already i.e as 3 & 4 but 5 in between them.

Hence the order before he moved cards must be as 3,5,4,2.

  Previous Order of The Cards