Question

the sum of the digits of a two digit no. is 9 also, nine times this no. is twice the no. obtained by reversing the order of the digits. Find the no. ​

Answer 1

Step-by-step explanation:

Let the unit digit be x and 10th place digit be y.

∴The number is 10y + x

If digits of the number is reversed then number becomes 10x + y.

Given that,

Sum of the digits of a two digit number. is 9

∴ x + y = 9 ---------------------------------(i)

Again,

Nine times the number is twice the number obtained by reversing the order of the digits.

∴ 9(10y + x) = 2(10x + y)

⇒90y + 9x = 20x +2y

⇒90y - 2y = 20x - 9x

⇒88y = 11x

⇒x= 8 ---------------------------------(ii)

Putting the value of x in equation(i), We get,

8 + y = 9

⇒y = 9 - 8

⇒y = 1

∴The number is 18

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