# Solution

(related to Problem: Domestic Economy)

Without the hint that I gave, my readers would probably have been unanimous in deciding that Mr. Perkins's income must have been £$1,710.$ But this is quite wrong. Mrs. Perkins says, "We have spent a third of his yearly income in rent," etc., etc.—that is, in two years they have spent an amount in rent, etc., equal to one-third of his yearly income. Note that she does not say that they have spent each year this sum, whatever it is, but that during the two years that amount has been spent. The only possible answer, according to the exact reading of her words, is, therefore, that his income was £$180$ per annum. Thus the amount spent in two years, during which his income has amounted to £$360,$ will be £$60$ in rent, etc., £$90$ in domestic expenses, £$20$ in other ways, leaving the balance of £$190$ in the bank as stated.

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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