Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number ?​

Answer 1

$\large\bf\underline {To \: find:-}$

• We need to find the two digit number.

$\large\bf\underline{Given:-}$

• Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
• found that the resulting new number is greater than the original number by 27.

$\huge\bf\underline{Solution:-}$

• Let the ten's place digit be x
• Let units place digit be y
• Number = 10x + y
• Reversed number = 10y + x

Sum of digits of a two digit number = 9

• x + y = 9
• x = 9 - y ......1)

❥ According to Question:-

if we interchange the digits then the new number is greater than the original number by 27.

➛ 10y + x = 10x + y + 27

➛ 9y - 9x = 27

putting value of x from 1)

➛9y - 9(9 - y) = 27

➛ 9y - 81 + 9y = 27

➛ 18y = 27 + 81

➛ 18y = 108

➛ y = 108 /18

➛ y = 6

putting value of y in 1)

➛x = 9 - y

➛x = 9 - 6

➛ x = 3

So

The original number(10x + y)= 10 × 3 + 6

• ❥ Original Number = 36

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Answer 2

$\bf\large{\underline{\underline{Question:-}}}$

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is

found that the resulting new number is greater than the original number by 27. What

is the two-digit number ?

$\bf\large{\underline{\underline{Given:-}}}$

• Sum Of Two Digit Is = 9
• On Interchanging The Digit , Resulting Number Is Greater Than Original Number By = 27

$\bf\large{\underline{\underline{To\:Find:-}}}$

• Original Two Digit Number = ?

$\bf\large{\underline{\underline{Procedure:-}}}$

Let the unit digit be y and tens digit be x

• Number formed = 10x + y
• Interchange number = 10y + x

★ x + y = 9 ( Given )------- equ(1)

$\sf→ 10y+x= 10x+y+27---equ(2)\\\sf→ 9y-9x=27\\\sf→ y-x=2-----equ(3)$

On solving equ(1) & equ(3)

we get,

→ x=3

→ y=6

$\bf\large{\underline{\underline{Hence:-}}}$

• Original number = 36
• Reverse number = 63