Exams

Given P = 54 and M = 80

According to the question,

Let ‘A’ years ago, M = 3P

=> M - A/P - A = 3

=> 80 - A = 3(54 - A)

=> 80 - A = 162 - 3A

=> 2A = 82

=> A = 41

Therefore, A = 41 years ago Sweety’s mother was 3 times of Sweety’s age.

Hence, at the age S = 13 and M = 39.

Let the distance in one direction = k kms

Speed in still water = 4.5 kmph

Speed of river = 1.5

Hence, speed in upstream = 4.5 - 1.5 = 3 kmph

Speed in downstream = 4.5 + 1.5 = 6 kmph

Time taken by Rajesh to row upwards = k/3 hrs

Time taken by Rajesh to row downwards = k/6 hrs

Now, required Average speed =$$\begin{gathered} Total distanceTotal speed = 2kk3 + k6 \\ = 2k x 186k + 3k = 4 kmph \end{gathered}$$ 

Therefore, the average speed of the whole journey = 4kmph.

Non collision can happen only when all the cars move in same direction.

That is either all cars moving in clockwise direction or all cars moving in anti clockwise direction.
P(all cars not colliding)

= P(all cars moving in the same direction)

= P(all cars moving in clockwise direction)  +  P(all cars moving in anticlockwise direction)

= [p(A --> C) x p(C --> B) x p(B --> A)]  +  [p(A --> B) x p(B --> C) x p(C --> A)]

= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]

= 1/8 + 1/8

= 1/4

The North American Free Trade Agreement (NAFTA) is an agreement signed by Canada, Mexico, and the United States and entered into force on 1 January 1994 in order to establish a trilateral trade bloc in North America.