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iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60782 Points
one year ago
Let the unit digit and tens digit of a number be x and y respectively. Then, Number (n) = 10B + A N after reversing order of the digits = 10A + B According to the given information, A + B = 9…………………….(i) 9(10B + A) = 2(10A + B) 88 B – 11 A = 0 -A + 8B = 0 ………………………………………………………….. (ii) Adding the equations (i) and (ii) we get, 9B = 9 B = 1……………………………………………………………………….(3) Substituting this value of B, in the equation (i) we get A= 8 Hence the number (N) is 10B + A = 10 x 1 +8 = 18

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