A censusman on duty visited a house which the lady inmates declined to reveal their individual
ages, but said — “we do not mind giving you the sum of the ages of any two ladies you may
choose”. Thereupon the censusman said — “In that case please give me the sum of the ages of
every possible pair of you”. The gave the sums as follows : 30,33,41,58,66,69. The censusman
took these figures and happily went away. How did he calculate the individual ages of the ladies
from these figures.

Question

A censusman on duty visited a house which the lady inmates declined to reveal their individual
ages, but said — “we do not mind giving you the sum of the ages of any two ladies you may
choose”. Thereupon the censusman said — “In that case please give me the sum of the ages of
every possible pair of you”. The gave the sums as follows : 30,33,41,58,66,69. The censusman
took these figures and happily went away. How did he calculate the individual ages of the ladies
from these figures.

goformit100 · Answer

@TessaMarie08181997 

@mikaela19900630 I personally tagged you too.

anonymous · Answer

http://www.artofproblemsolving.com/Forum/resources.php?c=78&cid=48&year=1990 go to this

anonymous · Answer

The sum of all the ages is  (30+33+41+58+66+69)/3=99
Looking which sum gives 99 gives 30+69+,33+66,41+58.
the ages are  $$a \le b \le c \le d $$
 this gives us a+b= 30 c+d=69
this solves to 11,19, 22,47

goformit100 · Answer

Thankyou Madam

anonymous · Answer

your welcome :)

anonymous · Answer

your welcome