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A number of two digits is such that four times the unit digit is five times greater than trice the tens digit. When the digits are reversed, the number is increased by nine find the number

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You said that
4u = 5*(3t)
10u+t = 10t+u + 9
This gives fractions for t and u. I think you must have meant

4u = 5+3t
10u+t = 10t+u + 9

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