Question
If 27 is subtracted from a two-digit number, its digits
get interchanged. Also, the sum of the digits of the number is 11. What is the number?Solution
Let the tens digit be x and units digit be y. Then number = 10x + y Given, after subtracting 27, digits get interchanged: 10x + y - 27 = 10y + x 9x - 9y = 27 x - y = 3 Also, x + y = 11 Now solving: x - y = 3 x + y = 11 2x = 14 x = 7 So, y = 4 Required number = 74 Hence, the correct answer is 74.
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