# Murder in a train

Five persons A,B,C,D,E are in a compartment in a train. A,C,E are men and B and D are women. The train passes through a tunnel and when it emerges, it is found that E is murdered. An enquiry is held. A, B, C, D make the following statements.

• A: I am innocent; B was talking to E when the train was passing through the tunnel.
• B: I am innocent; I was not talking to E when the train was passing through the tunnel.
• C: I am innocent; D committed the murder.
• D: I am innocent; one of the men committed the murder.

Four of these 8 statements are true and four are false. Assuming only one person committed the murder, who did it?

So, there are 8 statements.

A is making statement 1 and statement 2

B is making statement 1 and statement 2

C is making statement 1 and statement 2

D is making statement 1 and statement 2

one of the 1st statements is false and three are true. three of the 2dn statements are false and one is true.

This is given because four of the statements are true and four of them are false.

Now look at the second statement of A and B:

A says, “B was talking to E when the train was passing through the tunnel”

B says “I was not talking to E when the train was passing through the tunnel”

One statement is the negation of the the other.

If what A says is true then what B says is false

If what A says is false then waht B says is true.

Therefore one of these statements is true and one of them is false. If one of these statements are true, then the others must be false (this is because we we mentioned above, one of these statements is true and the other 3 are false.So the second statement of C and D are false.

Looking at the 2nd statement C made: “D committed the murder” is therefore false. So D did not commit the murder.

Looking at the 2nd statement of D: “one of the men committed the murder”. That is also false. So this means that a women commited the murder. Therefore A and C did not commit the murder.

This leaves us with B. So B must have committed the murder.