Puzzle | ( Distance, Time and Work)

Puzzle : (Distance) There is one scooter which has 2 tyres and one Stepney (i.e. total of 3 tyres). Each tyre can run up to maximum of 5 km. How long will the scooter run?
Solution :
7.5 km
EXPLANATION :
First, ride scooter for 2.5 km and change the 1st tyre with Stepney.
Now km remaining for 1st tyre is 2.5 km , 2nd tyre is 2.5 km and Stepney is 5 km
Again ride scooter for 2.5km and this time change 2nd tyre with 1st tyre.
Now km remaining for 1st tyre is 2.5 km, 2nd tyre is 0 km and Stepney is 2.5 km
Now ride 2.5km with remaining 1st tyre and Stepney.
Total = 2.5 + 2.5 + 2.5 = 7.5km

Puzzle : (Time and Work ) There is a room with two doors. One door empties the room in 6 minutes and the other one empties the room in 3 minutes. If both were open, how long would it take to empty the room ?
Solution :
2 minutes
EXPLANATION :
Door 1 takes 6 minutes to empty the room i.e.
1 min —— 1/6 empty
Thus, Door 1 can empty 1/6th of the people in a minute.
Door 2 takes 3 minutes to empty the room i.e.
1 min —— 1/3 empty
Thus, door 2 can empty 1/3rd of the people in a minute.
Therefore in 1 minute, both doors together can empty 1/6 + 1/3 = 1/2 of the people.
So it would take 1 more minute to evacuate the remaining 1/2 of the people.
Therefore, it takes 2 minutes to empty the room with both doors open.

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