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 Current Age Conclusion (Posted on 2013-09-10)
The birthdays of the five friends Al, Ben, Cal, Dan, and Ethan falls on the same day, though they are different ages.

On their mutual birthday, the five friends were discussing their respective current ages. The discussion was as follows:
```Dan said to Ben: "I'm nine years older than Ethan."
Ethan said to Ben: "I'm seven years older than Al."
Al said to Ben: "Your age is exactly 1.7 times that of mine."
Ben said to Cal: "Ethan is younger than you."
Cal said to Dan: "The difference between our ages is six years."
Cal said to Al: "I'm ten years older than you."
Cal said to Al: "Ben is younger than Dan."
Ben said to Cal: "The difference between your age and Dan's is the
same as the difference between Dan's and Ethan's."```
It is known that when one of them spoke to someone older, everything they said was true. However, when speaking to someone younger, everything they said was false.

What are the current ages of each person?

 See The Solution Submitted by K Sengupta Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution Comment 5 of 5 |

1) D=>B D=E+9

2) E=>B E=A+7

3) A=>B B=A*1.7

4) B=>C C>E

5) C=>D [C-D]=6

6) C=>A C=A+10

7) C=>A B<D

8) B=>C [C-D]=[D-E]

From above clues 6) is false so B>D and C>A hence from 1) D>E or ( E+9) and from 2) E>A or A+7 hence A<E<D<B

Possibilities of age of C are a) between E and D, b) Between D and B or c) older than B. for integer value of age of B only possibility is when A=30 then E=37, D=46 and B=51.

with possibility a) C-D=6 is true so C=40 which contradicts statements 4) and 8) same holds good for possibility b) hence c) is the only possibility so C=55.

 Posted by Salil on 2013-09-27 08:59:07

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