Dr. Johnson has won in a lottery.
He spends 4/5 of his money on a large house.
He spends ¾ of his remaining money on a yacht.
He spends 2/3 of his remaining money on travelling.
He gives the remaining $50,000 to charity.
How much money did he win?

See the answer

Answer: $3,000,000
Let X be the amount of money he won.
Then he spends 4/5 X on a house.
He spends ¾ (X – 4/5 X) = 3/20 X on a yacht.
He spends 2/3 of the remaining money on travelling and, therefore, gives 1/3 of the remaining money to charity. So we have, 1/3 (X – 4/5X – 3/20X) = 50,000.
Solving for X, we get  X = 3,000,000

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