Monday, August 16, 2010

Monday Puzzle: A Lady Never Tells Her Age

One day at the hairdresser, a beautician asked stately Mrs. Perkins how old she was. Mrs. P. glared at the woman over her glasses, and said "If you reverse the figures of my husband's age, you shall have mind."

This didn't satisfy the young woman at all, who said, "I don't know how old your husband is."

"I am younger than he. The difference between our ages is one-eleventh of their sum."

Mrs. P. thought this would confuse the hairdresser so much that she'd drop the subject, but the young woman did some quick calculations, smiled, and said, "I wouldn't worry about it, dear. You look very good for a woman of your age."

How old is Mrs Perkins?

3 comments:

Eye of the Frog said...

45, unfortunately brute forced.

Eye of the Frog said...

Had to go back to do my work :)

10x + y = wife
x + 10y = husband

((x + 10y) + (10x + y))/11 = (x + 10y) - (10x + y)
(11x + 11y)/11 = 9y - 9x
x + y = 9y - 9x
10x = 8y
5x = 4y
x = (4/5)y

wife = 8y + y
wife = 9y

husband = (4/5)y + 10y
husband = (54/5)y

(54/5)y - 9y = 11
54y - 45y = 55
11y = 55
y = 5

wife = 9y = 45
husband = (54/5)y = 54

Thomas L. McDonald said...

Impressively executed!

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