Question

a no consists of two digit whose sum is 9.if 9 is subtracted from the number it's digit are interchanged.find the number​

Answer 1

Answer :-

let the digit at ones place = n

let the digit at tens place = g

Number = 10g + n = 9

A.T.Q.

⠀⠀⟹ 10g + n - 9 = 10n + g

⠀⠀⟹ 10g + n - 10n - g = 9

⠀⠀⟹ 9g - 9n = 9

⠀⠀⟹ 9 (g-n) = 9

⠀⠀⟹ g - n = $\dfrac{9}{9}$

⠀⠀⟹ g - n = 1

⠀⠀⟹ g = n + 1

⠀⠀So , 10g + n = 9

⠀⠀⟹ n + 1 + n = 9

⠀⠀⟹ 2n + 1 = 9

⠀⠀⟹2n = 9 - 1

⠀⠀⟹ n = $\dfrac{8}{2}$

⠀⠀⠀⟹ n = 4

⠀⠀⠀⟹ g = 4 + 1

⠀⠀⠀⟹g = 5

hence ten's digit is 5 and units digit is 4 and number is 54