The difference between the two digits of a number
is 2. If the digits are reversed and the number added
to original numb

1 thought on “The difference between the two digits of a number<br />is 2. If the digits are reversed and the number added<br />to original numb”

1. Given:-

   • The difference between the two digits of a number is 2.
   • If the digits are reversed and the number is added to the original number, then the result is 132.

   To Find:-

   • The original number.

   Solution:-

   Let the digit in the ones place be y and the digit in the tens place be x.

   Hence,

   [tex]\dag{\boxed{\green{\rm{The\:original\:number = 10x + y}}}}[/tex]

   Now,

   On reversing the digits:-

   [tex]\dag{\boxed{\blue{\rm{The\:new\:number = 10y + x}}}}[/tex]

   Now,

   We are given that the difference between the two digits of the number is 2.

   Hence,

   [tex]\blue{\rm{10x – y = 2 \longrightarrow(i)}}[/tex]

   Also it is given that, the sum of original number and the new number is 132.

   Hence,

   [tex]\red{\rm{(10x + y) + (10y + x) = 132}}[/tex]

   [tex] = \red{\rm{10x + y + 10y + x = 132}}[/tex]

   [tex] = \red{\rm{11x + 11y = 132}}[/tex]

   [tex] :\implies \red{\rm{11(x + y) = 132}}[/tex]

   [tex] :\implies \red{\rm{x + y = \dfrac{132}{11}}}[/tex]

   [tex] = \red{\rm{x + y = 12 \longrightarrow(ii)}}[/tex]

   Now,

   On subtracting equation (i) from equation (ii)

   = (x + y) – (x – y) = 12 – 2

   = x + y – x + y = 10

   = 2y = 10

   [tex] = \sf{y = \dfrac{10}{2}}[/tex]

   = y = 5

   Putting the value of y in equation (i)

   = x – y = 2

   = x – 5 = 2

   = x = 2 + 5

   = x = 7

   Therefore the original number becomes:-

   • [tex]\rm{\orange{10x + y = 10\times 7 + 5 = 75}}[/tex]

   [tex]\boxed{\underline{\red{\rm{\therefore\:The\:original\:number\:is\:75}}}}[/tex]

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