RMO 1990 ; Part - 2
A census - man on duty visited a house in 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."
The census - man said, "In that case, give me the sum of the ages of every possible pair of you."
They gave the sum as follows : & .
The census - man then calculated their individual ages.
What is the number obtained by subtracting the smallest age from the largest one?
The answer is 36.
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1 solution
Let their ages be a, b, c, d with a<b<c<d. Then c + d is maximum followed byb + d and a + b is minimum followed by c + a. Then c + d = 69; a + b = 30; b + d = 66;a + c = 33. Then a +b +c+ d = 99.If a + b = 41 and b + c = 41 we get fractional values,neglect them and take a + d = 58 and b + c = 41 to get the required values