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 traveller wants to go from on 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?

• let number of direct roads between A and B = x
  B and C = y
  C and A = z
  x+z*y = 33 .......(1)
  y+x*z = 23 .........(2)
  on solving above equations we get z = 10/(y-x) +1
  z must be an integer as it indicates number of roads
  so y-x can be 1,2,5,10
  for y-x =2 equations (1) and (2) are satisfied
  => z = 6
• 8 years agoHelpfull: Yes(17) No(3)
• Here the person wants to travel from A to B(Via C):A........C.......B
  And From B to C( via A):B.........A..........C
  We have calculate ways between A&C
  i.e A.....C.....B-B.....A.....C= 33-23=10 Ways
  We have 10 ways from A to C
• 8 years agoHelpfull: Yes(4) No(7)
• ans :10
  33-23=10
• 8 years agoHelpfull: Yes(1) No(11)
• a----c-----b routes are 33
  b----a-----c routes are 23
  so in the 1st condition a-c 33 routes possible and the second a-c 23 possible outcomes....directly ...so ans is 56.
• 8 years agoHelpfull: Yes(0) No(9)