Q21. There are three cities A, B and C, each of these cities is connected with the other two cities by at least one direct road. If a traveler wants to go from one city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly there are 23 routes from B to C (including those via A). How many roads are there from A to C directly?
Q21. There are three cities A, B and C, each of these cities is connected with the other two cities by at least one direct road. If a traveler wants to go from one city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly there are 23 routes from B to C (including those via A). How many roads are there from A to C directly?
The correct option is A (a) 6
A) The possible figure can be: Number of ways of going from A to B can be 3, that of going from B to C can be 5, and finally that of A to C, can be 6. These are the only set of options that can satisfy the given conditions.
(a) 6
A)
The possible figure can be: Number of ways of going from A to B can be 3, that of going from B to C can be 5, and finally that of A to C, can be 6. These are the only set of options that can satisfy the given conditions.
