sum of digital of a two digit number is 11. If the digitals are interchange the number so got is 27 more than it. Find the numbers

2 thoughts on “sum of digital of a two digit number is 11. If the digitals are interchange the number so got is 27 more than it. Find the numbers”

1. Answer:

   Question :-

   • Sum of digital of a two digit number is 11. If the digitals are interchange the number so got is 27 more than it. Find the numbers?

   Given :-

   • Sum of digital of a two digit number is 11. If the digitals are interchange the number so got is 27 more than it.

   Find Out :-

   • Find the numbers?

   Solution :-

   Let :

   • Tens digit be x.
   • Ones digit be y.
   • Original number = 10x + y

   When digits are interchanged:

   [tex]\curlyeqsucc[/tex] New number = 10y + x

   Sum of two digit :

   [tex]\leadsto[/tex] x + y = 11

   [tex]\leadsto[/tex] x = 11 – y ———(Eqn no 1)

   When the digits are interchanged :

   [tex]\leadsto[/tex] 10x + y + 27 = 10y + x

   Substituting the value of x from eqn (i) we get that ,

   [tex]\leadsto[/tex] 10(11 – y) + y + 27 = 10y + 11 – y

   [tex]\leadsto[/tex] 110 – 10y + y + 27 = 9y + 11

   [tex]\leadsto[/tex] 137 – 9y = 9y + 11

   [tex]\leadsto[/tex] 9y + 9y = 137 – 11

   [tex]\leadsto[/tex] 18y = 126

   [tex]\leadsto[/tex] y = 126/18

   [tex]\leadsto[/tex] y = 7

   From the equation 1 we get,

   [tex]\leadsto[/tex] x = 11 – y

   Substituting the value of y = 7 in the equation no 1 we get,

   [tex]\leadsto[/tex] x = 11 – 7

   [tex]\leadsto[/tex] x = 4

   Let’s finding the original number:

   [tex]\implies[/tex] Original number = 10x + y

   [tex]\implies[/tex] Original number = 10(4) + 7

   [tex]\implies[/tex] Original number = 40 + 7

   [tex]\implies[/tex] Original number = 47

   Therefore, the numbers is 47.

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2. Answer:

   The number is 47

   Step-by-step explanation:

   Let,

   Units digit = x

   Tens digit = 11 – x

   Original number :

   ⇒ 10 (11 – x) + x

   ⇒ 110 – 10x + x

   ⇒ 110 – 9x

   If the digits are interchanged the number so got is 27 more than it

   ⇒ 10x + 11 – x

   ⇒ 10x – x + 11

   ⇒ 9x + 11

   ★ According to the Question :

   ⇒ (110 – 9x) + 27 = 9x + 11

   ⇒ 110 – 9x + 27 = 9x + 11

   ⇒ 110 + 27 – 9x = 9x + 11

   ⇒ 137 – 9x = 9x + 11

   ⇒ 137 – 11 = 9x + 9x

   ⇒ 126 = 18x

   ⇒ x = 126 / 18

   ⇒ x = 7

   Units digit = 7

   Tens digit = 11 – x

   ⇒ 11 – 7 = 4

   Tens digit = 4

   Therefore, the number is 47

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