Question

sum of digits of a two digit number is 9. when the digits are interchanged ,the new number is greater than the original number by 9. find the original number.
answer :45,54​

Answer 1

To Find :

• We have to find the original number .

Solution :

Let units place digit be y and ten's place digit be x.

Sum of digits of two digit number is 9.

• x + y = 9
• x = 9 - y ...1)

Number formed : 10x + y

$\underline{ \large \red{ \mathscr{A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

when the digits are interchanged ,the new number is greater than the original number by 9.

Reversed number : 10y + x

10x + y + 9 = 10y + x

10x - x + y - 10y = -9

9x - 9y = -9

9y - 9x = 9

• Substituting value of x from Equation (1)

9y -9(9 - y) = 9

9y - 81 + 9y = 9

18y = 9 + 81

18y = 90

y = 90/18

y = 5

• Substituting value of y in equation (1)

x = 9 - y

x = 9 - 5

x = 4

So,

Original number 10x + y :

= 10 × 4 + 5

= 45

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

⠀⠀⠀$\blue{\textrm{The original number is 45. }}$

$\blue{\textrm{And The Reversed number is 54. }}$

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