Question

Two birds are flying in opposite directions over the edge of a circle-shaped forest of radius 4 km. Both start off from the same point simultaneously and both have to go to the same nest. Who reaches the nest first?
I. Speed of bird A is 60 km/hr and speed of bird B is 50 km/hr.
II. The nest is dramatically opposite to the starting point of the flight of the two birds, on the circumference of the forest.
(a) If the question can be answered by anyone of the statements alone, but cannot be answered by using the other statement alone.
(b) If the question can be answered by using either statements alone.
(c) If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
(d) If the question cannot be answered even by using both the statements together.

Answer 1

Hint: We start solving the problem by drawing the figure representing all the given information. We then find the possible distances between the starting position of birds and the position of the nest they need to proceed. We then check whether we are given the paths that the birds follow to travel between those two points. Using these points we conclude and get the required answer.

Complete step-by-step answer:
According to the problem, we are given that two birds are flying in opposite directions over the edge of a circle-shaped forest of radius 4 km. Both start off from the same point simultaneously and both have to go to the same nest. We need to check whether we can find which bord reaches the nest first using the following statements.
I. Speed of bird A is 60 km/hr and speed of bird B is 50 km/hr.
II. The nest is dramatically opposite to the starting point of the flight of the two birds, on the circumference of the forest.
Let us draw the given information.

Let us assume that the birds start at point B and the nest is at point C.
Let us find the circumference of this circle-shaped forest, which is $2\pi \left( 4 \right)=8\pi km$.
The distance between the points B and C along the circumference of the circle is $\dfrac{8\pi }{2}=4\pi km$.
We can also see that the distance between point B and C is equal to the diameter of the circle. i.e., $2\times 4=8km$.
We can see that we get different answers if the birds move in diameter, moving by following the circumference of the circle. We don’t know what is the exact path followed by each bird. So, we cannot solve this problem by taking two statements together.
So, the correct option for the given problem is (d).

So, the correct answer is “Option (d)”.

Note: We should know that the path is very important in finding the time to travel between two points. As we can see that the travel time will change following different paths between two points. We should not just assume that the birds follow the circular path i.e., along the circumference of the circular forest as it will make a big difference in the problem. Whenever we get this type of problem, we need to check each small detail that any contradiction may occur.