Question
A two-digit number is 4 times the sum of its digits. If 27 is added to the number, the digits interchange their places. What is the number?
Solution
ATQ, Let the number be 10x + y. Condition 1: 10x + y = 4(x + y) => 10x + y = 4x + 4y => 6x = 3y => y = 2x Condition 2: (10x + y) + 27 = 10y + x => 9y - 9x = 27 => y - x = 3 Substitute y = 2x: 2x - x = 3 x = 3. Then y = 2(3) = 6. The number is 36.
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