A man, starting from a point P, takes exactly six equal steps. Each step is in one of the four directions – East, West, North and South. What is the total number of ways in which the man ends up at point P after the six steps?
(a) 200 (b) 256 (c) 400 (d) 512
Four vehicles are travelling on a straight highway with constant speeds.The trucks overtook the car at 2:00 Pm and then met the scooter at 4:00 PM and the motorcycle at 6:00 PM.The motorcycle met the car at 7:00 pm then it overtook the scooter at 8:00.At what time scooter and the car meet?Choose one answer.
a. 5:00 pm b. 5: 40 pm c. 5: 30 pm d. 5: 20 pm
Solution
Truck--> X. X.
-----------------------.-----------------------
Car(2pm)-->.
The above fig is as per question: let distance travelled by truck in 2 hrs be X
1) Motorcycle meets car at 7 pm
Hence distance travelled by motorcycle in 1 hr + distance travelled by car in 5 hrs = X+X =2X
I.e 1M+5C = 2X
=> M=2X - 5C...........(1)
2) Motorcycle overtakes scooter at 8 pm
Hence distance travelled by motorcycle in 2 hrs - distance travelled by scooter in 4 hrs = X
I.e. 2M - 4S = X
=> M= (X+4S)/2.........(2)
Now from (1) and (2), we get
2X - 5C = (X+4S)/2
=> 3X =10C+4S
=> X = (10/3) C + (4/3) S
This means that car will meet scooter when car will travel for (10/3) hrs after 2 pm I.e. 5.20 pm
Or
Scooter will travel for (4/3) hrs after 4 pm I.e again 5.20 pm
Hence answer is D
P.s. apologies for posting it late. @shivamarora @nitya101289 @vidit9811
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