Tricky Ratios
Mr Hony, Mr Potts and Mr. Turner spend the evening gambling at home. At the start of the evening the amount of money they have between them is in the ratio 5 : 4 : 3, respectively, while at the end of the evening the amount of money is in the ratio 4 : 3 : 2, respectively.
One of them loses 1$. How much money did they have at the start of the evening altogether?
The answer is 36.
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1 solution
Let start with 1st H:P:T = 5x : 4x : 3x, in the end = 4y : 3y : 2y so H+P+T = 12x = 9y --> 4x = 3y so the one who loses 1 $ must be Mr. Turner (Mr. Hony : 5x-4y is not a positive value, and Mr. Potts 4x = 3y ) so ... 3x-2y = 1 3(3/4)y - 2y = 1 y = 4 the answer (the sum of money) = 9y (4y + 3y + 2y) = 36