Question

Eight railway stations A, B, C, D, E, F, G and H are connected either by two way passage or one way passages.One way passages are from C to A, E to G,B to F, D to H, G to C, E to C and H to G. Two way passages
are between A and E, G and B, F and D, and E and D.

ques -While travelling from C to H, which one of the following
stations must be passed through.

(a) G
(b) E
(c) B
(d) F

In how many different ways can a train travel from F to A without passing through any station more than once?
(a) 1
(b) 2
(c)3
(d)4​

Answer 1

Given

Total number of stations = 8

Total number of passages = 2

One way passage =  C to A, E to G,B to F, D to H, G to C, E to C and H to G

Two way passage = between A and E, G and B, F and D, and E and D.

To find:

While travelling from C to H, which stations must be passed through.

In how many different ways can a train travel from F to A without passing through any station more than once.

Solution:

One way passage connections -

C-A , E-G , B-F , E-C , H-G , D-H , G-C

Two way passages -  

A=E , G=B , E=D , F=D

1. If we want to travel from c to h there is only one possibility to go to A.

From A only one to go to E. Thus, it needs to pass through E.

2. Following the path - F-D-E-C-A, F-D-H-G-C-A, F-D-E-G-C-A  or F-D-E-A

Thus total ways = 4

Answer 2

1) E must be passed.

2) Two routes are possible.

Step-by-step explanation:

Given: One way passages of trains are:

C to A

E to G

B to F

D to H

G to C

E to C

H to G.

Two way passages of trains are:

A = E

G = B

F = D

E = D

Solution:

1) C to H should pass through....

C to A = E = D to H

E must be passed. Option b is the answer.

2) F to A

Route one is: F = D to H to G to C to A

Route two is: F = D = E = A

Two routes are possible. Option b is the answer.